If they get stuck, you might say: Let's work backwards. Suppose you ask how many words can be made that start with AT, for instance. Clearly there are four: ATA, ATG, ATT, and ATC. This is true for any first pair. So we conclude that there are four times as many words as there are first pairs. Now we need to figure out how many first pairs there are. If you start with A, there are four AA, AG, AT, and AC. For each of these pairs, there are four complete three-word pairs. So, for words beginning with A, there are 4 x 4 or 16 words. The same must be true for words beginning with G, T, and C, for a total of 16 + 16 + 16 + 16 or 64 different words.