Answer
$x=8$
Work Step by Step
Separate the square roots on two sides. Then square both sides and combine like terms. When down to the last square root, square both sides again to solve.
$\sqrt {x+8}-\sqrt {x-4}=2$
$\sqrt {x+8}=2+\sqrt {x-4}$
$(\sqrt {x+8})^2=(2+\sqrt {x-4})^2$
$x+8=4+4\sqrt {x-4}+x-4$
$8=4\sqrt {x-4}$
$\sqrt {x-4}=2$
$x=8$
