Here we need to find the area of the shaded part of the square. For finding the area of the shaded region we can find the area of the bigger square and the smaller square and then subtract the area of the smaller square from area of the larger square.

Area of the larger square =$x^2$
                                     = $8^2$
                                     = 64$c{m}^2$

Area of the smaller square = $b^2$
                                       = $4^2$
                                       = 16 $c{m}^2$

The area of the shaded region will be = Area of the bigger square – Area of the smaller square
                                 = 64 – 16
                                 = 48 $c{m}^2$
Therefore the area of the shaded region will be 48$c{m}^2$.