There are several ways to find the area of the frame:
(the picture is arbitrarily in landscape format for the descriptions below)
(1) Area of 4 square corners=4x2; top and bottom strips=12x; side strips=8x. Total area: 20x+4x2.
(2) Area of top and bottom strips including corners=2x(6+2x)=12x+4x2; side strips=8x. Total area: 20x+4x2.
4x2+20x=24in2 (given), x2+5x-6=0=(x+6)(x-1), so x=1" (the other value is negative, so is meaningless).
(a) The area of the inner rectangle is the area of the picture=4×6=24in2.
(b) The width of the strip (frame)=1" (see calculations above).