It is a scalar quantity.
Step 2: Electric flux through square
Suppose a cube enclosing the charge q of side d.
Hence according to Gauss's law, the electric flux through the cube is qϵo
The given case can be considered as one of the face of such a cube.
By symmetry, the flux through the face is 16th of the flux through the cube.
Hence flux through the square face = q6ϵo
Part (b)
Electric flux through square when the side is doubled
Now, the charge is placed at a distance d from the centre of square. Also, the side of the square is 2d in this case.
In this case, the charge will be at the center of a cube of side 2d and the square will be one of its face.
According to a similar analysis as shown in Step 2 the electric flux through the face is: q6ϵo
Hence there will be no change in the electric flux.