Answer
$\Phi = -16~N~m^2/C$
Work Step by Step
$E = 4.0 \hat{i}+3.0(y^2+2.0)~\hat{j}$
Note that the electric flux through the top face and the bottom face is zero, since the z component of the electric field is zero.
We can find the electric flux through the back face:
$\Phi = (4.0)~\hat{i}~\cdot -A~\hat{i}$
$\Phi = -4.0~A$
$\Phi = -(4.0)~(2.0~m)^2$
$\Phi = -16~N~m^2/C$
