Break the question into two parts. First, what is the probability that the coin turns up tails on the first flip? That's 1/2.

Second, what is the probability that the coin turns up tails on at least one of the following two flips? When you see the words "at least," look for the opposite. The only way that coin does NOT turn up heads at least once is if it turns up tails both times. The probability of that is (1/2)(1/2) = 1/4. That's what we don't want to happen; the probability of what we DO want to happen is the opposite: 1 - 1/4 = 3/4.

Thus, we need two things to happen. The probability of the first is 1/2, and the probability of the second is 3/4. Since both must occur, multiply the probabilities together: (1/2)(3/4) = 3/8, choice (C).