Answer
$$18$$
Work Step by Step
Consider $g(x,y,z) =z$
Solve the flux of $F$ .
$$\iint_{S} F \cdot n \ d \theta =3 \times \iint_{R} \ dy \ dx \\=\int_0^{2} \int_{0}^{3} 3 \ dy \ dx \\ = \int_0^{2} [ 3y]_{0}^{3} \ dx \\= \int_0^{2} 3(3-0) \ dx \\=9 \times [x]_0^2 \\=18$$
