[tex]\huge\boxed{-14}[/tex]
We have the following equation:
[tex]h(f)=-2(f+5)^2+4[/tex]
Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.
[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]
