Box A is a cube with surface area=6×144=864 sq in, because each face has an area of 12²=144 sq in and there are 6 faces. An expression for the surface area is 6×12×12 (part A). Algebraically the surface area of a cube is 6a² where a is the side length.
Box B has a square top and bottom each 256 sq in, making 512 sq in in total. The four sides each have the same area: 16×6.75=108 sq in, so the total area for the 4 sides=4×108=432 sq in. The total surface area is 432+512=944 sq in.
(A cube always has the minimum surface area for maximum volume, compared with a cuboid or rectangular prism.) An expression for the surface area is 2×16²+4×16×6.75, which could be written 2×16(16+2×6.75) (part B); or algebraically, 2a(a+2h) where a is the square side and h the height.
(C) The most economical is Box A with SA 864 sq in, compared with Box B with SA 944 sq in.