Answer
$\Phi = 24~N~m^2/C$
Work Step by Step
$E = 4.0 \hat{i}-3.0(y^2+2.0)~\hat{j}$
We can find the electric flux through the left face where $y=0$:
$\Phi_l = -3.0(y^2+2.0)~\hat{j}~\cdot -A~\hat{j}$
$\Phi_l = 3.0(0^2+2.0)~\hat{j}~\cdot A~\hat{j}$
$\Phi_l = (6.0)~(2.0~m)^2$
$\Phi_l = 24~N~m^2/C$
