Answer
$$= 32 \pi $$
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
$$ Flux =\iiint_{o}(2x+3) \space dz \space dy \space dx \\ =\nabla \cdot F \\=\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{2} (2 \rho \sin \phi \cos \theta+3) \space (\rho^2 \sin \phi) \space d\rho \space d\phi \space d\theta \\ =\int_{0}^{2 \pi}(4 \pi \cos \theta +16) d\theta \\= 32 \pi $$
