Ok, so:
We flip a coin twice.
The probability to get a head first will be 1/2. That's because we have 1 favorable case over 2 possible cases.
In the second flip, we want to get a tail, so:
The probability to get a tail will be 1/2. That's because we have 1 favorable case over 2 possible cases.
Now, the probability of that events happen one and then other, will be given by the following events:
It could be that first, we get a tail and then a tail.
It could be that first, we get a tail and then a head.
It could be that first, we get a head and then a tail.
It could be that first, we get a head and then a head.
Looking at these possibilities, there's only one we need as a favorable case, over 4 possible cases.
So, we conclude that the probability of this, is 1/4. Which is the same than multiplying (1/2)*(1/2).