Answer
$$4xy-4y^2$$
Work Step by Step
We know the following equation for the area of the shaded region:
$$ A_{shaded}=\text{Overall Area} - \text{ Area Used Up}$$
Using this, we find:
$$x^2-(x-2y)^2 \\x^2-\left(x^2-4xy+4y^2\right) \\ 4xy-4y^2$$
