Answer
$18$
Work Step by Step
We have: $g(x,y,z) =z$
We set up the integral and solve the flux of $F$ as follows:
$\iint_{S} F \cdot n \ d \theta =\iint_{R} 3 \ dy \ dx$
or, $=\int_0^{2} \int_{0}^{3} 3 \ dy \ dx$
or, $= \int_0^{2} [ 3y]_{0}^{3} \ dx$
or, $= \int_0^{2} 3(3-0) \ dx$
or, $=[ 9x]_0^2$
or, $=18$
