Certification Pursuant to Rule 30a-2(b) under the 1940 Act and Section 906
of the Sarbanes-Oxley Act
I, James M. Dykas, Chairman of the Board, President and Chief Executive Officer of First Trust Enhanced Equity Income Fund (the “Registrant”), certify that:
| 1. | The Form N-CSR of the Registrant (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 Registrant. |
| Date: | | September 9, 2024 | | /s/ James M. Dykas | |
| | | | | James M. Dykas, President and Chief Executive Officer
(principal executive officer) | |
I, Derek D. Maltbie, Treasurer, Chief Financial Officer and Chief Accounting Officer of First Trust Enhanced Equity Income Fund (the “Registrant”), certify that:
| 1. | The Form N-CSR of the Registrant (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 Registrant. |
| Date: | | September 9, 2024 | | /s/ Derek D. Maltbie | |
| | | | | Derek D. Maltbie, Treasurer, Chief Financial Officer
and Chief Accounting Officer
(principal financial officer) | |
