jmc

Two side lengths are straightforward. We have $AB=15$ because the $y$-coordinates of $A$ and $B$ are the same and their $x$-coordinates differ by 15. Similarly, the $y$-coordinates of $B$ and $C$ differ by 8 and their $x$-coordinates are the same, so $BC=8$. We could either notice that $△ABC$ is right, or use the distance formula (i.e., the Pythagorean Theorem) to see that $$AC=\sqrt{(9-(-6){)}^2+(-2-6{)}^2}=\sqrt{15^2+(-8{)}^2}=17.$$ So, the perimeter of $ABC$ is $15+8+17=\boxed{40}$.