subtract 3x-12/4x^2-8*2x^2-4/9x-36

As written, I get

-19x^2 + (23/9)x - 36

Assuming the usual sloppiness with parentheses, I'll assume you meant

(3x-12)/(4x^2-8)*(2x^2-4)/(9x-36)
=
3(x-4)*2(x^2-2)
----------------------
4(x^2-2)*9(x-4)

= 1/6