Answer: 13.7345175425633 square feet
The rounding instructions are cut off, so it's not clear how you want to round this.
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Step-by-step explanation:
The area of the square is 8*8 = 64 square feet.
The two unshaded semicircles combine to form a full circle of radius 4 ft. This circle has an area of A = pi*r^2 = pi*4^2 = 16pi square feet.
The shaded area is the result of taking the circle area away from the larger square area
shaded area = (area of large square) - (area of two semicircles)
shaded area = (area of large square) - (area of circle with radius 4)
shaded area = 64 - 16pi = exact value
shaded area = 13.7345175425633 = approximate value