Use the Divergence Theorem to calculate the surface integral

Question

S
F · dS;
that is, calculate the flux of F across S.
F(x, y, z) = x^4i − x^3z^2j + 4xy^2zk,

S is the surface of the solid bounded by the cylinder
x^2 + y^2 = 4
and the planes
z = x + 6 and z = 0.