Answer
$\frac{256 \pi}{15}.$
Work Step by Step
The volume is given by
$$
\pi \int_{0}^{2}\left(4-x^{2}\right)^{2} d x=\pi \int_{0}^{2}\left(16-8 x^{2}+x^{4}\right) d x\\=\left.\pi\left(16 x-\frac{8}{3} x^{3}+\frac{1}{5} x^{5}\right)\right|_{0} ^{2}=\frac{256 \pi}{15}.
$$
