As we know that, total flux due to a charge enclosed in a region is given as ϕ=Qε0 (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 ϕ=Q8ε0.Since three faces don't have any effect, the flux will be divided into three parts again.
Therefore, total flux will become, ϕ=Q24ε0
The correct option A.