#### Answer

$x=-10$

#### Work Step by Step

Change base $9$ on the right side to match base $3$ on the left side by making it $3^2$. Then apply the distributive property, cancel out the bases, and set the sides equal to each other. Then solve for $x$.
$3^{x-2}=9^{x+4}$
$3^{x-2}=(3^2)^{x+4}$
$3^{x-2}=3^{2x+8}$
$x-2=2x+8$
$x=-10$