Nonlinear functions SAT question

The correct answer is $76$. It's given that the graph of $y=g(x)$ is the result of translating the graph of $y=f(x)$ up $4$ units in the xy-plane. It follows that the graph of $y=g(x)$ is the same as the graph of $y=f(x)+4$. Substituting $g(x)$ for $y$ in the equation $y=f(x)+4$ yields $g(x)=f(x)+4$. It's given that $f(x)=(x-6)(x-2)(x+6)$. Substituting $(x-6)(x-2)(x+6)$ for $f(x)$ in the equation $g(x)=f(x)+4$ yields $g(x)=(x-6)(x-2)(x+6)+4$. Substituting $0$ for $x$ in this equation yields $g(0)=(0-6)(0-2)(0+6)+4$, or $g(0)=76$. Thus, the value of $g(0)$ is $76$.