That's the problem. I got an answer of -2 which I am not sure of. Help me please.
-2 does not lie in the domain of this function as it causes division by 0 on the RHS
$\displaystyle
\frac{1}{x-2} = \frac{3}{x+2} - \frac{6x}{(x-2)(x+2)}$
$\displaystyle
\frac{x+2}{(x+2)(x-2)} = \frac{3(x-2)}{(x-2)(x+2)} - \frac{6x}{(x-2)(x+2)}$
The denominator cancels
$\displaystyle x+2 = 3x-6-6x$
$\displaystyle x = -2$
That's unusual...