What values are zero for the function g(x) = (x^2 +4x-12)(x-3)

(x+6)(x-2)(x-3) therefore the zeros are -6, 2, and 3

Let's factor the first parenthesis.
X^2 + 4x -12
For this, we need to find what multiplies to -12, but adds to 4. (This skill gets faster and easier through time, but I will just tell you know the numbers are 6 and -2)

So it becomes:
(X+6)(x-2)(x-3)

So your roots are:
6, -2, and 3.

I hope this Helps!