Suppose h12->z/12z is a homomorphism of groups.Prove that g(t^2)=[0] mod 12

My attempt so far is
g(t6) = [0]9

by Homomorphism
g(a*b)=g(a) * g(b)

g(t^2*t^2*t^2) = g(t2) *g(t2)*g(t2)
g(t6)
0 = 3g(t2)