I don't know how to get the inverse laplace transform of this
F(S)= .(s+1)^2
. . ---------
. . (s+2)^4
Maybe it will become clearer if you split it up into partial fractions:
$\displaystyle \frac{(1+s)^2}{(s+2)^4} = \frac{1}{(s+2)^2} - \frac{2}{(s+2)^3} + \frac{1}{(s+2)^4} $
Let me know if you're still stuck as I've worked through the question.
Another hint if you want it:
Spoiler: