Answer
No solution
Work Step by Step
$$\frac{-2}{x-3}+\frac{3}{x+3}=\frac{-12}{(x+3)(x-3)}$$
$$(x+3)(x-3)(\frac{-2}{x-3}+\frac{3}{x+3})=(x+3)(x-3)(\frac{-12}{(x+3)(x-3)})$$
$$-2(x+3)+3(x-3)=-12$$
$$-2x-6+3x-9=-12$$
$$x-15=-12$$
$$x=3$$
However, 3 is an extraneous solution. There is no solution.