What am I doing wrong?

original problem:
x^2-144/x+4 times x^2-16/x+12

This is what I have so far:
(x+12)(x-12)/x+4 times (x-8)(x+2)/x+12

I don't know if this is right or what to do from here.

((x+12)(x-12)/(x+4))*(x-8)(x+2)/(x+12),

Cancel factors (x+12)and get:

(x - 12) (x - 8) (x + 2) / (x + 4).