What are the excluded values of x for x+4/-3x^2+12x+36

I will assume that you meant:

(x+4) / (-3x^2+12x+36) factor the denominator ...

(x+4) / (-3 (x^2-4x-12))

To factor a quadratic of the form ax^2+bx+c you need to find two values, j and k, which satisfy two conditions ...

jk=ac=-12 and j+k=b=-4 so j and k must be 2 and - 6 and the factors are then:

(x+2) (x-6) so we are now left with:

(x+4) / (-3 (x+2) (x-6))

The only restriction on this function is that division by zero is undefined, so x cannot equal - 2 or 6