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: July 17, 2008                    /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: July 17, 2008                     /s/ Mark R. Bradley
      -------------                    -----------------------------------------
                                        Mark R. Bradley, Treasurer, Controller,
                                        Chief Financial Officer and Chief
                                        Accounting Officer
                                        (principal financial officer)