Answer
$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$
Work Step by Step
$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}$
Take out common factor $2x(x+6)^{3}$ from the numerator and simplify:
$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(x+6)^{3}[(x+6)-2x]}{(x+6)^{8}}=...$
$...=\dfrac{2x(x+6)^{3}(-x+6)}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$
