Answer
$x=0$ satisfies the given conditions.
Work Step by Step
$y=(x+4)^{3/2}$ and $y=8$
Substitute $y$ by $8$:
$(x+4)^{3/2}=8$
Raise both sides to $\dfrac{2}{3}$:
$[(x+4)^{3/2}]^{2/3}=8^{2/3}$
$x+4=\sqrt[3]{8^{2}}$
$x+4=4$
Solve for $x$:
$x=4-4$
$x=0$
$x=0$ satisfies the given conditions.