EXHIBIT (b)


      Certification Pursuant to Rule 30a-2(b) under the 1940 Act and
                  Section 906 of the Sarbanes-Oxley Act

I, James A. Bowen, Chairman of the Board, President and Chief Executive Officer
of First Trust/Four Corners Senior Floating Rate Income Fund II (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: January 26, 2009

                                     /s/ James A. Bowen
                                     ----------------------------------------
                                     James A. Bowen, Chairman of the Board,
                                     President and Chief Executive Officer
                                     (principal executive officer)



I, Mark R. Bradley, Treasurer, Controller, Chief Financial Officer and Chief
Accounting Officer of First Trust/Four Corners Senior Floating Rate Income Fund
II (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: January 26, 2009

                                     /s/ Mark R. Bradley
                                     ----------------------------------------
                                     Mark R. Bradley Treasurer, Controller,
                                     Chief Financial Officer and
                                     Chief Accounting Officer
                                     (principal financial officer)