Answer
$\dfrac{dy}{dx}=2.$
Work Step by Step
$\dfrac{d}{dx}((4-x)y^2)=\dfrac{d}{dx}(x^3)\rightarrow$
$-y^2+\dfrac{dy}{dx}(2y(4-x))=3x^2\rightarrow$
$\dfrac{dy}{dx}=\dfrac{3x^2+y^2}{8y-2yx}.$
At $(2, 2)\rightarrow\dfrac{dy}{dx}=\dfrac{3(2)^2+2^2}{8(2)-2(2)(2)}=2.$