Answer
$$\dfrac{-40}{3}$$
Work Step by Step
We know that $$ div F=\dfrac{\partial P}{\partial x}i+\dfrac{\partial Q}{\partial y}j $$
From the given equation, we have $$ Flux =\iiint_{o} -x \space dA \\=\nabla \cdot F \\ =\int_{0}^{2}\int_{0}^{\sqrt {16-4x^2}}\int_{0}^{4-y} (-x) \space dz \space dx \space dy \\\int_{0}^{2}(\dfrac{x\sqrt {16-4x^2}}{2}-4x (16-4x^2)^{1/2} \space dx \\= \dfrac{-40}{3}$$
