Many of these types of counting questions can be resolved by thinking about the number of possible symbols in each slot. In this case, since our radio station call code must have 4 letters, we have 4 slots:
_ _ _ _
But instead of filling each slot with a possible letter from A to Z, we're going to fill it in with the number of possible letters that can go in that slot.
Since the first letter must be a K or W, the first slot has two options:
2 _ _ _
Now that we've "placed" the first letter, the second slot only has 25 options left, since the second letter must be different from the first, and there are only 26 letters in the alphabet (assuming this radio station is in an English-speaking country). So we have:
2 25 _ _
Now that we've placed the second letter, the third slot only has 24 options, since we've already placed two letters, and the third one has to be different from the first and the second:
2 25 24 _
Finally, our last slot only has 23 options, since we've already used three different letters for the first three slots:
2 25 24 23
The final flourish is to simply multiply all of these options together. This gives us:
2 x 25 x 24 x 23 = 27,600
So the number of different 4-letter radio station call codes satisfying the conditions above is 27,600.