On a GRE problem you have to works always outside in. Starting from what you know and find a path

Here we do know that area overall and the base

Now the area formula is \(A=\frac{1}{2} *b*h\)

\(2 \sqrt{3} =\frac{1}{2} *2 *h\) and what we are looking for at the moment is the h

Simplify and we have \(h=2 \sqrt{3}\)

Considering we have the base which is 2 and the h of the triangle which is 2 3 we can find the missing side

\(2^2+(2 \sqrt{3} )^2= 4+4*3=\sqrt{16}=4\)

Now we have all the pieces of the puzzle

\(\frac{1}{2} * 4 * h = 2\sqrt{3}

h =\sqrt{3}\)

I hope now is clear