Compute the Flux of the Vector Field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$

Short Answer

Compute the flux of the vector field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.
What is the answer if the plane is oriented downward?