Let each square be divided into 4 equal parts....so we have 4 squares * 4 parts each = 16 total parts
In the top left square, using symmetry, 1 of the 4 parts is shaded
And the same for the bottom right square
And for the top right square, 2 of the 4 parts are shaded
And the same for the bottom left square
So...the shaded portion is
[ 1 + 1 + 2 + 2] / 16 =
6 /16 =
3 / 8