#### Answer

The solution is $x=16$

#### Work Step by Step

$\sqrt{x}-\sqrt{x-12}=2$
Take $\sqrt{x-12}$ to the right side:
$\sqrt{x}=2+\sqrt{x-12}$
Square both sides:
$(\sqrt{x})^{2}=(2+\sqrt{x-12})^{2}$
$x=4+4\sqrt{x-12}+x-12$
Leave the term with the square root alone on the right side of the equation:
$x-4-x+12=4\sqrt{x-12}$
$8=4\sqrt{x-12}$
Take $4$ to divide the left side:
$\dfrac{8}{4}=\sqrt{x-12}$
$2=\sqrt{x-12}$
Square both sides:
$2^{2}=(\sqrt{x-12})^{2}$
$4=x-12$
Rearrange:
$x-12=4$
Solve for $x$:
$x=4+12$
$x=16$
The solution is $x=16$