Well if he has \(12\) shirts, he has \(12\) to choose from. So \(12\) for the first choice, \(11\) for the second choice (because the first has been used), and \(10\) for the third choice. Thus, he has \(12\cdot11\cdot10\) choices, but they are counted \(6\) times each, so the answer is \(\boxed{220}\).