The prisoners know that there are only two hats of each color. So if D observes that B and C have hats of the same color, D would deduce that his own hat is the opposite color. However, if B and C have hats of different colors, then D can say nothing. The key is that prisoner C, after allowing an appropriate interval, and knowing what D would do, can deduce that if D says nothing the hats on B and C must be different; able to see B's hat, he can deduce his own hat color.