Answer: 6 because: 

You can choose the first letter any of 3 ways.
Then for each of those 3 ways you can choose the first
letter, that leaves 2 ways you can pick the second letter,

So that answer is 3×2 or 6.  Here are all 6 two-letter
permutations listed:

1. TA
2. TX   <-- when T was chosen as the 1st, that left 2, A and X, for the 2nd
3. AT
4. AX   <-- when A was chosen as the 1st, that left 2, T and X, for the 2nd
5. XA
6. XT   <-- when X was chosen as the 1st, that left 2, A and T, for the 2nd

3 ways to choose the first letter TIMES 2 ways to choose the second letter,
and 3×2 = 6.  So you don't have to list them to find out how many there are,
you can just multiply 3 by 2.

Edwin