The cans must be arranged in a 12x1, 6x2, or a 4x3 pattern. The perimeter of the 12x1 arrangement will be 2x(24+2), since each can has a two-inch diameter, thus 52 inches. The 6x4 pattern will give a perimeter of 32 inches 2x(12+4). The 4x3 pattern has a perimeter of 2x(8+6) or 28 inches. So, 4x3 cans has the smallest perimeter. (Notice the area is constant, so the perimeter will be minimized when length and width are most nearly equal.)
The lateral area is 28 inches x 8 inches (perimeter times height) or 224 square inches.
The surface area is the lateral area plus the two bases (top and bottom) which is 224 square inches plus 2x(6x8) or 96 square inches, thus 320 square inches.
