#### Answer

$b=8\sqrt 2$

#### Work Step by Step

According to the Pythagorean Theorem, if $a$ and $b$ are the lengths of the shorter sides of a right triangle and $c$ is the length of the longest side, then $a^{2}+b^{2}=c^{2}$.
Therefore, $4^{2}+b^{2}=12^{2}$.
$16+b^{2}=144$
Subtract 16 from both sides.
$b^{2}=128$
Take the square root of both sides.
$b=\sqrt 128=\sqrt (64\times2)=\sqrt 64\times\sqrt2=8\sqrt 2$