This is a problem of composition of functions. So, we have the following equations:
[tex]r(x)=2x+2[/tex]
[tex]s(x)=-2x^{2}-2[/tex]
First of all, we find the value of r(4), that is, substituting x = 4 in the equation we have:
[tex]r(4)=2(4)+2=10[/tex]
Then we find s(r(4)) that is equal to s(10), therefore substituting x = 10 in the equation we have:
[tex]s(r(4))=s(10)=-2(10)^{2}-2=\boxed{-202}[/tex]
