A charge $Q$ is kept at the corner of a cube. Electric flux passing through one of those faces not touches that charge is:-

As we know that, total flux due to a charge enclosed in a region is given as $\varphi =\frac{Q}{{\epsilon }_0}$ (Gauss's law)

Here, the charge is on a corner of each of the 8 cubes.

Hence, an equal amount of flux will spread outwards through each of the cubes due to symmetry.

Hence,  the magnetic flux through each cube is given as $\varphi =\frac{Q}{8{\epsilon }_0}$.

Since three faces don't have any effect, the flux will be divided into three parts again.

Therefore, total flux will  become,  $\varphi =\frac{Q}{24{\epsilon }_0}$

The correct option A.