The best estimate of the area of the picture is 600 square inches.
The total area of the picture is the sum of the area of the trapezoid and the area of the two semicircles.
The area of the trapezoid is equal to 1/2 * base * height = 1/2 * (12 + 24) * 10 = 180 square inches.
The area of one semicircle is equal to 1/2 * pi * radius^2 = 1/2 * pi * 12^2 = 72 pi square inches.
The total area of the two semicircles is equal to 2 * 72 pi square inches = 144 pi square inches.
The total area of the picture is equal to 180 square inches + 144 pi square inches.
The value of pi is approximately 3.14, so the total area of the picture is approximately 180 + 144 * 3.14 = 600 square inches.
The best estimate of the area of the picture is 600 square inches.