#### Answer

$= \frac{6h(h-3)}{(h+4)(h+8)}$

#### Work Step by Step

$\frac{h^{2}-7h+12}{h^{2}+2h-8} \div \frac{h^{2}+4h-32}{6h^{2}-12h}$
$= \frac{h^{2}-7h+12}{h^{2}+2h-8} \times \frac{6h^{2}-12h}{h^{2}+4h-32}$
$= \frac{(h-3)(h-4)}{(h+4)(h-2)} \times \frac{6h(h-2)}{(h+8)(h-4)}$
$= \frac{(h-3)(h-4)}{(h+4)} \times \frac{6h}{(h+8)(h-4)}$
$= \frac{(h-3)}{(h+4)} \times \frac{6h}{(h+8)}$
$= \frac{6h(h-3)}{(h+4)(h+8)}$