I am working on the red-shaded problem below however I am unsure how to use my answer from part b to answer the question. Any help is appreciated.

I am working on the red-shaded problem below however I am unsure how to use my answer from part b to answer the question. Any help is appreciated.

Well, $Y(s) = H(s) * F(s)$.
So then the response $y(t)$ can be determined by inverting $Y(s) = H(s) * F(s) = H(s) * U(s) $, where $ U(s) $ is the Laplace Transform of the Heaviside function.