First of charge doesn't have units of micro farad it must be micro coulomb.

 

Now consider cube of side 10cm enclosing the charge of 10 micro coulomb at the centre which is at a distance 5cm from each of the sides.

 

Now applying gauss's law of electrostatics

 

Electric Flux passing through the cube = q/₀.

 

But by symmetry of the problem the flux is equidistributed through each sides.

 

Thus flux through the square plate of side 10cm = q/6₀

 

or flux = 10^(-6)/6₀.