Answer
$4$
Work Step by Step
Recall that $2^3=8$, thus:
$8^{\frac{2}{3}}=(2^3)^{\frac{2}{3}}$
Now, recall the basic exponent property (pg. 360):
$(a^m)^n=a^{mn}$
Applying this property, $\left(2^3\right)^{\frac{2}{3}}$ simplifies to:
$=(2)^{\frac{3\cdot 2}{3}}$
$=(2)^{\frac{6}{3}}$
$=(2)^{2}$
$=4$