Answer
This equation has no solution
Work Step by Step
$\dfrac{3}{x+2}+\dfrac{2}{x-2}=\dfrac{8}{(x+2)(x-2)}$
Multiply the whole equation by $(x+2)(x-2)$:
$(x+2)(x-2)\Big[\dfrac{3}{x+2}+\dfrac{2}{x-2}=\dfrac{8}{(x+2)(x-2)}\Big]$
$3(x-2)+2(x+2)=8$
$3x-6+2x+4=8$
Take all terms without $x$ to the right side of the equation and solve for $x$:
$3x+2x=8+6-4$
$5x=10$
$x=\dfrac{10}{5}$
$x=2$
Since the original equation is not defined for $x=2$, it has no solution.