Answer
$4\sqrt{3}\text{ inches}$
Work Step by Step
Let $x$ be the unknown side of the given right triangle. By the Pythagorean Theorem, $a^2+b^2=c^2$, then,
\begin{array}{l}
x^2+4^2=8^2
\\\\
x^2=8^2-4^2
\\\\
x^2=64-16
\\\\
x^2=48
\\\\
x=\sqrt{48}
\\\\
x=\sqrt{16\cdot3}
\\\\
x=4\sqrt{3}\text{ inches}
.\end{array}
