In a region of space, the electric field is in the x-direction, proportional to x and given by $\overrightarrow{E}=\alpha x\widehat{i}$ where $\alpha$ is a positive constant. Consider an imaginary cubical volume of edge $a$ with its edges parallel to the axes of coordinates. The charge inside this cubical volume is

The field at the face ABCD$=\alpha x_0\widehat{i}$

So, flux over the face ABCD$=-\left(\alpha x_0\right)a^2$

The negative sign arises as the field is directed into the cube

The field at the face $EFGH=\alpha (x_0+a)\widehat{i}$

So, flux over the $EFGH=\alpha (x_0+a)a^2$

The flux over the other four faces is zero as the field is parallel to the surfaces

So, total flux over the cube$=\alpha a^3=\frac{q}{{\epsilon }_0}$ where q is the total charge inside the cube

 $\Rightarrow q={\epsilon }_0\alpha a^3$