(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.