Answer
$4x^{4}$
Work Step by Step
The area of a square , Area = $side$ X $side$
Here, $side$ = $2x^{2}$
Hence, Area = $2x^{2}$ X $2x^{2}$
This becomes : Area = $2$ X $2$ X $x^{2}$ X $x^{2}$ = $4x^{2+2}$=$4x^{4}$
(Since the exponents are added while multiplying with the same base)
Final result : Area = $4x^{4}$