Answer
$$12 \pi$$
Work Step by Step
$$Volume=\iint_{x^2+y^2 \leq 4} \int_{0}^{3-y} dz dA\\=\iint_{x^2+y^2 \leq 4} (3-y) dA \\=3 \iint_{x^2+y^2 \leq 4} dA - \iint_{x^2+y^2 \leq 4} y dA$$
The inner integral is the integral of an odd continuous function in a symmetric interval; this implies that $\iint_{x^2+y^2 \leq 4} y dA=0$
and $$Volume=(3) \times (\pi) \times (2)^2 -0=12 \pi$$
