Hint: You will factor using difference of squares and a=1 methods.
(f / g) (x) = x^2 - 16 (x + 4) ( x - 4) x + 4
___________ = ______________ = ______
x^2 - 6x + 8 (x - 2) (x - 4) x - 2
The key to this type of problem is to factor the difference of squares first, and then see if you can use one of these factors to factor the trinomial in the denominator...