Transform the differential equation into an algebraic equation by taking the Laplace transform of each side. Use $Y$ for the Laplace transform of $y$, (not $Y(s)$).

$=$

Therefore

$\displaystyle Y =$

$\displaystyle =$ $\frac{1}{s-6}+$ $\frac{1}{s+6}+$ $\frac{1}{s+2}$

Taking the inverse Laplace transform we get
$y =$