Answer
$g(x)=\sqrt[3]{\frac{x+6}{2}}$
Work Step by Step
$f(x)=2x^3-4$
$(f\circ g)(x)=x+2$
$g(x)=y=?$
The composition of the two functions is represented as:
$(f\circ g)(x)=f(g(x))$
$f(y)=2(y)^3-4$
$x+2=2y^3-4$
Solve this equation for $\ y\ $ to get:
$x+6=2y^3$
$y^3=\frac{x+6}{2}$
$y=\sqrt[3]{\frac{x+6}{2}}$
$g(x)=\sqrt[3]{\frac{x+6}{2}}$