Answer
$a=4$
Work Step by Step
The given equation is
$\Rightarrow 4-\sqrt a=2$
Add $\sqrt a-2$ to each side.
$\Rightarrow 4-\sqrt a+\sqrt a-2=2+\sqrt a-2$
Simplify.
$\Rightarrow 2=\sqrt a$
Square each side of the equation.
$\Rightarrow 2^2=(\sqrt{a})^2$
Simplify.
$\Rightarrow 4=a$
Check $a=4$.
$\Rightarrow 4-\sqrt a=2$
$\Rightarrow 4-\sqrt 4=2$
$\Rightarrow 4-\sqrt {2^2}=2$
$\Rightarrow 4-2=2$
$\Rightarrow 2=2$
True.
Hence, the solution is $a=4$.
