#### Answer

(a) $60$, $(-6,60)$.
(b) $-4$, $(-4,12)$.

#### Work Step by Step

(a) Given $H(x)=(\frac{1}{2})^x-4$, we have $H(-6)=(\frac{1}{2})^{-6}-4=60$ which gives point $(-6,60)$.
(b) $12=(\frac{1}{2})^x-4$, thus $x=-4$ which gives point $(-4,12)$ on the graph.