I have to simplify 3y^2-12y/9y^3, I just can't seem to figure out how to simplify the 9y^3.

I assume the problem is

(3y^2) - (12y/y^3) =
Then you handle the second term:
-12y/9y^3 =
divide 12 and 9 by 3 to give
-4y/3y^3
then divide y in the numerator into y^3 in the denominator to give
-4/3y^2.
You may want to move the 3y^2 out from the denominator; if so, just multiply the entire equation by 3y^2.