Multiply the rational expression: 12f -16/ 16 divided by 5/9f^2 - 16

It would help if you'd please use parentheses to indicate clearly what is to be multiplied or divided by what.

I am assuming (not claiming that I know) you meant:

(12f-16)                     (5)
divided by
      16                        9f^2 - 16

Factor as much as possible before attempting division:

4(3f-4)                     5
divided by
     16                     (3f-4)(3f+4)

This is equivalent to multiplying as follows:

4(3f-4)      (3f-4)(3f+4)
*
   16                       5

Is this what you meant?  If so, please finish the work.  If not, please copy down the original problem making liberal use of parentheses for clarity.