SILGAN HOLDINGS INC. 4 Landmark Square Suite 400 Stamford, CT 06901

Exhibit 10.6

SILGAN HOLDINGS INC.

4 Landmark Square

Suite 400

Stamford, CT 06901

April 12, 2011

Blackstone Capital Partners III Merchant Banking Fund L.P.

c/o Blackstone Management Associates III L.L.C.

345 Park Avenue

New York, New York 10154

Attention: Chinh Chu

Ladies and Gentlemen:

Reference is made to that certain Agreement and Plan of Merger, dated as of the date hereof (the “Merger Agreement”), by and between Silgan Holdings Inc. (“Parent”), a Delaware corporation, and Graham Packaging Company Inc. (the “Company”), a Delaware corporation, pursuant to which the Company will merge with and into the Parent with the Parent being the surviving corporation. In the event of any conflict between this letter agreement (this “Agreement”) and the Merger Agreement, the terms of the Merger Agreement shall prevail. Capitalized terms used herein and not otherwise defined shall have the meanings set forth in the Merger Agreement.

By execution below, simultaneous with the execution of the Merger Agreement, each of Parent, and Blackstone Capital Partners III Merchant Banking Fund L.P. (the “Stockholder”) agree as follows:

1. Board Nominee. (a) Pursuant to the terms of that certain Amended and Restated Stockholders Agreement dated as of November 6, 2001 (the “Principals Stockholders Agreement”), by and among R. Philip Silver (“Co-Founder 1”), D. Greg Horrigan (“Co-Founder 2” and, together with Co-Founder 1, the “Co-Founders”) and the Parent, the Group (as such term is defined in the Principals Stockholders Agreement and generally including the Co-Founders and their affiliates, family members, trusts and estates) has the right to nominate for election all of the members of the Board of Directors of the Parent (the “Parent Board”) so long as the Group holds an aggregate of at least one-half of the shares of the Parent’s common stock, par value $.01 per share (“Common Stock”) held by it on February 14, 1997 (as adjusted, if necessary to take into account any stock dividend, stock split, combination of shares, subdivision or recapitalization of the capital stock of the Parent). Pursuant to the terms of that certain Stockholders Agreement, dated as of even date herewith (the “Stockholders Agreement”), by and among the Stockholder, the Co-Founders and the Parent, the Stockholder is entitled to designate for nomination one individual (the “Stockholder Nominee”) as a member of the Parent Board, who the Co-Founders shall subsequently nominate for election as a member of the Parent Board pursuant to the terms of the Principals Stockholders Agreement.

(b) Parent shall take all action necessary to cause the Stockholder Nominee to be appointed to the Parent Board as a Class I Director, effective as of the first day immediately following the day on which the Effective Time occurs.

(c) (i) In the event that the Group no longer has the right to nominate to stand for election all of the directors of the Parent Board under the terms of Section 2.1(a) of the Principals Stockholders Agreement, until such date that the Stockholder holds less than one-third of the number of

shares of Common Stock held by it in the aggregate as of the Effective Time of the Merger (as adjusted, if necessary, to take into account any stock dividend, stock split, combination of shares, subdivision or recapitalization of the capital stock of the Parent) (such date, the “Termination Date”), the Stockholder shall have the right to designate a Stockholder Nominee and upon such designation by the Stockholder such Stockholder Nominee shall be nominated by the Parent, in accordance with the Parent’s nominating and governance policies and so long as such Stockholder Nominee is reasonably acceptable to the Parent Board or any nominating committee thereof, to stand for election as a member of the Parent Board. Upon such nomination by the Parent, such Nominee shall stand for election as a member of the Parent Board in accordance with the Parent Certificate. In the event that a Stockholder Nominee does not meet the requirements of the Parent’s nominating and governance policies and/or is not reasonably acceptable to the Parent Board or any nominating committee thereof, the Stockholder shall have the right to designate a different individual as a Stockholder Nominee until a Stockholder Nominee does meet the nominating and governance policies of the Parent and/or is reasonably acceptable to the Parent Board or any nominating committee thereof, as applicable. The Stockholder Nominee shall be nominated by the Parent Board or any nominating committee thereof as a Class I Director (as such term is defined in the Parent Certificate). Parent hereby agrees that Mr. Chinh Chu (“Mr. Chu”) is deemed reasonably acceptable for purposes hereof.

(ii) In the event that the Group no longer has the right to nominate to stand for election all of the directors of the Parent Board under the terms of Section 2.1(a) of the Principals Stockholders Agreement, prior to the Termination Date, the Stockholder shall provide Parent with its designee for Stockholder Nominee within 30 days of receipt of a written request from Parent for such designee’s name, provided that Parent shall not deliver such notice more than 90 days prior to the applicable annual meeting of the stockholders of the Company. If the Stockholder fails to designate a Stockholder Nominee to stand for election as a member of the Parent Board at such meeting within such 30 day period and the Group no longer has the right to nominate all of the directors to stand for election to the Parent Board under the terms of Section 2.1(a) of the Principals Stockholders Agreement, then the Parent shall have the right, in lieu of the Stockholder, to nominate to stand for election as a member of the Parent Board, in accordance with the Company’s nominating and governance policies and the Parents Certificate, such individual that the Stockholder so failed to designate.

(iii) If the Stockholder Nominee is not Mr. Chu, on the first anniversary of such Stockholder Nominee either being elected or appointed to the Parent Board, if such Stockholder Nominee is not reasonably satisfactory to a majority of the Parent Board (excluding the Stockholder Nominee), then the Stockholder shall cause such Stockholder Nominee to resign immediately. The Stockholder may designate an individual to be nominated to fill such vacancy created by the resignation of such Stockholder Nominee in accordance with the terms of Section 1(c)(i) of this Agreement or the Stockholders Agreement, as applicable, but only so long as the Stockholder has the right to designate for nomination one individual to the Parent Board pursuant to the terms hereof or thereof, as applicable, and provided that if any such replacement Stockholder is not Mr. Chu, if on the first anniversary of such replacement Stockholder Nominee either being elected or appointed to the Parent Board, such Stockholder Nominee is not reasonably satisfactory to a majority of the Parent Board (excluding the Stockholder Nominee), then the Stockholder shall cause such Stockholder Nominee to resign immediately and the Stockholder may designate an individual to be nominated as provided above in this clause (iii) and such Stockholder Nominee shall be subject to removal as provided herein.

(d) In the event that (A) a Stockholder Nominee dies, resigns or is otherwise removed by the Stockholder and (B) the Group no longer has the right to nominate to stand for election all of the directors of the Parent Board under the terms of Section 2.1(a) of the Principals Stockholders Agreement then, prior to the Termination Date, the Stockholder shall have the right to designate such Nominee’s replacement, in accordance with the Parent’s nominating and governance policies, the Parent

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Certificate and the Parent’s bylaws and so long as such Stockholder Nominee is reasonably acceptable to the Parent Board or any nominating committee thereof. In the event that a replacement Nominee is not reasonably satisfactory to the Parent Board or any nominating committee thereof, the Stockholder shall have the right to designate a different individual as a replacement Nominee until a replacement Nominee is reasonably satisfactory to the Parent Board or any nominating committee thereof.

(e) Immediately following the Termination Date, the Stockholder will cause the Stockholder Nominee to resign as a member of the Parent Board.

(f) Parent hereby agrees that in addition to any regular cash annual retainer fees and meeting fees normally paid to all members of the Parent Board, if any annual awards of restricted stocks or restricted stock units or any other equity awards are granted to non-employee directors of the Parent Board, in lieu thereof, the Stockholder Nominee will be entitled to an additional cash fee in an amount equal to the fair market value thereof, determined as of the date of grant in accordance with Parent’s practices.

2. Standstill. (a) From the Effective Time until such time as the Stockholder beneficially owns less than 5% of the outstanding voting securities of Parent (such period, the “Standstill Period”) the Stockholder agrees that without the prior written consent of the Parent Board, none of the Stockholder or its affiliates will in any manner, directly or indirectly, (i) by purchase or otherwise, acquire, or agree to acquire, ownership (including, but not limited to, beneficial ownership) of any equity securities issued by Parent or any direct or indirect rights (including, without limitation, any convertible, derivative or synthetic securities) or options to acquire (or otherwise act in concert with any person which so acquires, offers to acquire or agrees to acquire) such ownership (other than solely from a stock split, dividend or recapitalization; or any rights granted to all stockholders of Parent); (ii) submit any proposal for, or otherwise offer to enter into, a transaction with Parent involving the acquisition (by merger, tender offer, purchase, statutory share exchange or otherwise) of ownership (including, but not limited to, beneficial ownership) of any securities issued by Parent; (iii) acquire or effect control of Parent or directly or indirectly form, join, participate or encourage the formation of any group (other than with its affiliates) within the meaning of Section 13(d)(3) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) with respect to any voting securities of Parent or in order to acquire or affect control of Parent; (iv) other than with respect to the election of the Stockholder Nominee, directly or indirectly solicit proxies or become a participant in any proxy solicitation or any election contest or seek to advise or influence any person with respect to the voting of any securities issued by Parent; or (v) initiate, propose or solicit votes for stockholder proposals or induce or attempt to induce any other person to initiate any stockholders proposal (other than any stockholder proposals recommended by the Parent Board); (vi) call or seek to have called any meeting of the stockholders of Parent or execute any written consent in lieu of a meeting of holders of any securities of Parent; (vii) other than the Stockholder Nominee, seek election or seek to place a representative on the Parent Board or seek the removal of any member of the Parent Board, in any case alone or in concert with others; (viii) otherwise, directly or indirectly, alone or in concert with others, seek to control the management, Board or policies of Parent (provided that the designation of the Stockholder Nominee pursuant hereto and such Stockholder Nominee’s service on the Parent Board shall not be deemed a breach of this clause (viii)); or (ix) make any public announcement with respect to any of the foregoing; provided that the restrictions contained in clause (i) above shall not in any way limit the activities of any affiliates of the Stockholder in the businesses distinct from the private equity business.

(b) Notwithstanding the foregoing clause (a), the Standstill Period shall terminate and the restrictions on the Stockholder set forth in clause (a) above shall have no further force and effect in the event that (i) Parent files a petition in bankruptcy or for similar relief, is adjudicated bankrupt or insolvent, consents to the appointment of a receiver or similar official, makes a general assignment for the

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benefit of its creditors, or a bankruptcy petition with regard to Parent is not discharged or denied within 90 days; (ii) Parent is in material breach of the registration rights agreement entered into between Parent and Stockholder as of the date hereof and such breach is not cured within 30 days of written notice thereof, or (iii) Parent breaches in any material respect its obligations under the Stockholders Agreement, or fails to include on the slate of directors the Stockholder Nominee nominated by the Co-Founders pursuant to the terms of the Stockholders Agreement and the Principals Stockholder Agreement and in accordance with the Parent Certificate, or support such Stockholder Nominee’s election to the Parent Board, which breach or failure is not cured within 30 days of written notice thereof.

3. Voting Agreement. (a) The Stockholder hereby agrees that, during the Standstill Period, at any meeting of the stockholders of Parent, however called, including any adjournment or postponement thereof, the Stockholder shall, in each case to the fullest extent that the Covered Shares (as hereinafter defined) are entitled to vote thereon, or in any other circumstance in which the vote, consent or other approval of the stockholders of Parent is sought, (i) appear at each such meeting or otherwise cause the Covered Shares beneficially owned by the Stockholder as of the applicable record date to be counted as present thereat for purposes of calculating a quorum; and (ii) vote (or cause to be voted), in person or by proxy, all of such Covered Shares as of the applicable record date:

(A) in favor of any slate of nominees standing for election to the Parent Board that is recommended by the Parent Board and submitted to the vote of the stockholders of Parent;

(B) with respect to any Approved Transaction (as hereinafter defined), either, at the Stockholder’s sole discretion, (I) in favor of such Approved Transaction or (II) proportionate with the manner in which all holders of Common Stock (other than the Stockholder) vote with respect to such matter; and

(C) with respect to any Disapproved Transaction (as hereinafter defined), against such Disapproved Transaction.

(b) For purposes hereof:

(i) “Approved Transaction” means any merger, consolidation or other business combination, tender offer, exchange offer, recapitalization, reorganization or any transaction involving the purchase or acquisition of equity or direct or indirect purchase or acquisition of assets recommended by the Parent Board and submitted to the vote of the stockholders of Parent.

(ii) “beneficial ownership” of any securities means ownership, directly or indirectly, through any contract, arrangement, understanding, relationship or otherwise, where the Stockholder has or shares with another Person (A) voting power which includes the power to vote, or to direct the voting of, such security; and/or (B) investment power which includes the power to dispose, or to direct the disposition, of such security; and shall otherwise be interpreted in accordance with the term “beneficial ownership” as defined in Rule 13d-3 adopted by the SEC under the Exchange Act; provided that for purposes of determining beneficial ownership, the Stockholder shall be deemed to be the beneficial owner of any securities which may be acquired by such Person pursuant to any agreement, arrangement or understanding or upon the exercise of conversion rights, exchange rights, warrants or options, or otherwise (irrespective of whether the right to acquire such securities is exercisable immediately or only after the passage of time, including the passage of time in excess of 60 days, the satisfaction of any conditions, the occurrence of any event or any combination of the foregoing). The terms “beneficially own”, “beneficial owner” and “beneficially owned” shall have a correlative meaning.

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(iii) “Covered Shares” means shares of securities of Parent beneficially owned by the Stockholder. In the event of a stock split, stock dividend or distribution, or any change in the securities of Parent by reason of any split-up, reverse stock split, recapitalization, combination, reclassification, exchange of shares or the like, the term “Covered Shares” shall be deemed to refer to and include such shares as well as all such stock dividends and distributions and any securities into which or for which any or all of such shares may be changed or exchanged or which are received in such transaction.

(iv) “Disapproved Transaction” means any merger, consolidation or other business combination, tender offer, exchange offer, recapitalization, reorganization or any transaction involving the purchase or acquisition of shares or direct or indirect purchase or acquisition of assets submitted to the vote of the stockholders of Parent but not recommended by the Parent Board.

(c) The Stockholder hereby covenants and agrees that, except for this Agreement, it shall not (i) enter into at any time while this Agreement remains in effect, any voting agreement, voting trust or similar arrangement with respect to any Covered Shares, and (b) grant at any time while this Agreement remains in effect, a proxy, consent or power of attorney with respect to any Covered Shares (other than as contemplated by clause (a) above).

4. Remedies. (a) In the event that any covenant or agreement in this Agreement is not performed in accordance with its terms, each party hereto agrees that, in addition to any other remedy at law or in equity, the non-breaching party will have the right to an injunction, temporary restraining order, specific performance or other equitable relief in any court of competent jurisdiction enjoining any such breach and enforcing specifically the terms and provisions hereof. Each party hereto agrees not to oppose the granting of such relief in the event a court determines that such a breach has occurred, and to waive any requirement for the securing or posting of any bond in connection with such remedy.

(b) All rights, powers and remedies provided under this Agreement or otherwise available in respect hereof at law or in equity shall be cumulative and not alternative, and the exercise or beginning of the exercise of any thereof by any party shall not preclude the simultaneous or later exercise of any other such right, power or remedy by such party.

5. Effectiveness of this Agreement. This Agreement shall become effective only upon the Effective Time of the Merger and shall have no force or effect until such time or in the event the Effective Time does not occur. Section 1 of this Agreement shall continue in effect until the Termination Date, at which time Section 1 of this Agreement shall terminate and be of no further force or effect. Sections 2 and 3 of this Agreement shall terminate upon the termination of the Standstill Period, at which time Sections 2 and 3 shall be of no further force and effect. At the time that Sections 1, 2 and 3 of this Agreement have terminated, this entire Agreement shall be deemed terminated and shall have no further force and effect.

6. Miscellaneous. (a) This Agreement may not be amended, supplemented or modified except in writing, duly executed by all of the parties.

(b) This Agreement and the Stockholders Agreement constitute the entire agreement of the parties with respect to the subject matter hereof. Each of the parties represents that they has been advised by counsel in connection with their review, execution and delivery of this Agreement.

(c) This Agreement is made in New York and shall be governed by and construed in accordance with the internal substantive laws of the State of New York.

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(d) This Agreement may be executed in more than one counterpart. Each such counterpart shall be deemed an original and all counterparts, taken together, shall constitute one and the same instrument.

(e) Neither this Agreement nor any rights or obligations hereunder shall be assigned by any party without the prior written consent of the other party.

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IN WITNESS WHEREOF, the parties have caused this Agreement to be executed in multiple originals by their authorized officers, all as of the date and year first written above.

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