Answer
$\Phi = 0$
Work Step by Step
$E = 4.0 \hat{i}-3.0(y^2+2.0) \hat{j}$
Note that the electric field only has components along the x axis and the y axis. The component of the electric field along the z axis is zero.
We can find the electric flux through the top face:
$\Phi = E~A~cos~90^{\circ}$
$\Phi = 0$