How can I solve inequaltion?

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.

sorry for any inconvenience this may have caused try again

try again.