P and Q are the centers of the two semicircles.
Draw BP perpendicular to AC.
BP is radius to the semi-circle. So are AP and PC.
Therefore, BP = AP = PC = 2 units.
In semicircle ABC, area of the shaded portion is the difference between the area of half the semicircle PBC and the area of the triangle PBC.
Triangle PBC is a right triangle because PB is perpendicular to PC. PB and PC are radii to the circle and are equal. So, triangle PBC is an isosceles triangle.
Therefore, triangle PBC is a right isosceles triangle.
Area of the semicircle ABC = ½ area of the circle of radius 2.
So, area of half the semicircle, PBC = ¼ area of the circle of radius 2.
Area of half the semicircle, PBC = ¼ * π * 2^{2}
Area of half the semicircle, PBC = π sq units
Area of right triangle PBC = ½ PC * PB
Area of triangle PBC = ½ * 2 * 2 = 2 sq units
Area of shaded region in one of the semi circles ABC = (π - 2) sq units
Therefore, area of the overall shaded region = 2(π - 2) sq units
Choice C is the correct answer.