Let's call the width of the base "w" and the length of the base "l". Since the perimeter of the base is 80 inches, this means that 2w + 2l = 80. We are also told that the length is 4 times the width, so l = 4w. We can substitute this second equation into the first equation to get 2w + 2(4w) = 80, which simplifies to 10w = 80. Dividing both sides by 10, we find that w = 8 inches. The width of the base is 8 inches, so the length of the base is 4 * 8 inches = 32 inches. The volume of the rectangular aquarium is the product of the base's area and the height of the aquarium, so it is (32 inches * 8 inches) * 12 inches = 3072 cubic inches. Therefore, the volume of the aquarium is 3072 cubic inches.