Exhibit 32.4

CERTIFICATION PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT

In connection with the Annual Report of Highwoods Realty Limited Partnership (the “Operating Partnership”) on Form 10-K for the period ended December 31, 2012 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Terry L. Stevens, Senior Vice President and Chief Financial Officer of Highwoods Properties, Inc., general partner of the Operating Partnership, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Operating Partnership.

/s/ Terry L. Stevens

Terry L. Stevens

Senior Vice President and Chief Financial Officer of the General Partner

February 12, 2013