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A point charge q is placed at the centre...

A point charge q is placed at the centre of the edge of a cubical box. Find the total flux associated with that box.

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If q is placed as shown, three more identical cubes are required to enclose. That charge completely. Then the total flux through all faces of 4 cubes is `(q)/(in_(0))`. Now contribution of this flux through each cube (given) is `(q)/(4 in_(0))`. Here it is interesting to note that the faces which have common edge on which the given charge is kept have no flux and hence the flux `(q)/(4in_(0))` emerges through the remaining four faces of the cube.
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AAKASH SERIES-ELECTRIC CHARGES AND FIELDS-Practice Exercise
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