Okay, so I need to figure out how many license plates can be formed with the format: 2 different letters followed by 2 different one-digit numbers. Let me start by breaking down the problem into parts. 

First, the license plate has two parts: the letters part and the numbers part. Let's tackle each part separately. 

Starting with the letters. The problem says there are two different letters from A to Z. There are 26 letters in the English alphabet. Since they have to be different, the first letter can be any of the 26, and the second letter can be any of the remaining 25. So, for the letters part, the number of possible combinations should be 26 * 25. Let me check that. Yeah, because for the first position, there are 26 choices, and for the second position, since one letter is already used, there are 25 left. So that gives 26 multiplied by 25. Let me calculate that: 26 * 25 = 650. So there are 650 possible combinations for the letters part.

Now moving on to the numbers part. It says two different one-digit numbers, which are from 0 to 9. So there are 10 possible digits. Similarly, the first digit can be any of the 10, and the second digit can be any of the remaining 9. So the number of combinations here is 10 * 9. Let me verify. 10 options for the first digit, then 9 for the second. So 10 * 9 = 90. That seems right. 

Now, since the letters and numbers are separate parts of the license plate, the total number of license plates would be the product of the two combinations. So, the total number of license plates is 650 (letters) multiplied by 90 (numbers). Let me compute that. 650 * 90. Hmm, 650 times 90. Let's break it down: 600 * 90 = 54,000 and 50 * 90 = 4,500. Adding them together: 54,000 + 4,500 = 58,500. So the total number of license plates is 58,500. 

Wait, let me double-check my calculations. 26 letters, 2 different, so 26P2 = 26*25 = 650. Then 10 digits, 2 different, so 10P2 = 10*9 = 90. Then total combinations 650*90. Let me compute 650 * 90 again. 650 * 9 = 5,850, so 5,850 * 10 = 58,500. Yep, that's correct. 

Is there any possibility I missed something? For example, are the letters and numbers required to be in a specific order? The problem states "2 different letters... followed by 2 different one-digit numbers". So the order is fixed: letters first, then numbers. So there's no need to consider permutations of the entire license plate, just the two separate parts. 

Another thing to check: are the letters allowed to be uppercase or lowercase? The problem says "A through Z", which are uppercase, but usually license plates can have both cases. However, the problem specifies "A through Z", so maybe only uppercase letters are considered. The problem statement doesn't mention case sensitivity, so I assume it's just uppercase letters. Similarly, digits are specified as 0-9, so case isn't an issue here. 

Therefore, I think my calculation is correct. The total number of license plates is 58,500.
</think>