Answer
$$30$$
Work Step by Step
We have: $g(x,y,z) =y$
Solve the flux of $F$.
$$I=\iint_{S} F \cdot n \ d \theta =2 \times \iint_{R} \ dz \ dx \\=(2) \times \int_{-1}^{2}\int_2^7 \ dz \ dx \\= 2 \times \int_{-1}^{2} [ z]_{2}^{7} \ dx \\= \int_{-1}^{2} 2(7-2) \ dx \\= \int_{-1}^{2} 10 x \ dx \\=10 \times [x]_{-1}^{2} \\=30$$
