The area of the square is 6 x 6 = 36 square inches.
There are two semi circles which would make a complete circle.
Area of a circle is PI x r^2
The diameter of the circle is the length of the side of the square, the radius is half of that, so r = 3
Area of the circle is 3.14 x 3^2 = 3.14 x 9 = 28.26 square inches.
The space in the square not taken up by the circle would be 36 - 28.26 = 7.74 square inches.
The shaded portion is half of that:
Shaded portion = 7.74 / 2 = 3.9 square inches.