Answer
$\frac{-2x}{(x+6)^4}$
Work Step by Step
We factor out $(x+6)$ and cancel with the denominator. Then we simplify:
$\displaystyle \frac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\frac{(x+6)^{3}[2x(x+6)-4x^{2}]}{(x+6)^{8}}=\frac{2x^{2}+12x-4x^{2}}{(x+6)^{5}}=\frac{12x-2x^{2}}{(x+6)^{5}}=\frac{2x(6-x)}{(x+6)^{5}}=\frac{-2x}{(x+6)^4}$
