$h(2)=\sqrt{4}=2$
$g(f(2))=?$

$f(2)=2(2)+5=9$
$g(9)=?$

$f(g(\sqrt{x+2}))$

$g(\sqrt{x+2})=\sqrt{x+2}^2-1=x+1\text{, so}$

$f(x+1)=?$

$g(2x+5)=?$

Set your expression from part (c) equal to $48$ and solve for $x$.