two states have different rules for

Dear Sachin9,

I'm happy to help with this.

This IR question is essentially a double "counting" problem. You may find this blog helpful:
https://magoosh.com/gmat/2012/gmat-quant-how-to-count/
That article discusses the FCP --- I will use this in both problems.

In State A, a license plate has 7 digits. The first 3 digits are letters, but the first letter cannot be an A, B, or C. The remaining digits are all numbers and zeros are not allowed.
First of all, here's my literal reading of the problem.
For the first slot has 23 possibilities (every letter except A, B, or C). Each of the next two has 26 possibilities --- there is no information forbidding repeat letters. MMM could be a legitimate choice for the first three letters. Then, for each of the remaining four slots, the number slots, there are 9 possibilities in each, every number except zero. This yields a total number of possibilities of
23*26*26*9*9*9*9 = 23*(26^2)*(9^4)

What you say in the spoiler section is 100% correct. We completely agree on this calculation.

I think the problem is the font or layout in this question box. Specifically, when they write
262*94*23
I think what they are trying to say is
(26^2)*(9^4)*23

Throughout the answer choices, wherever 263 appears, apparently they mean 26^3, and wherever 94 appears, apparently they mean 9^4. That the only thing that makes the OA make any sense as all.

You didn't specify a source for this question. I would say --- if they can't even print exponents correctly, I would consider this prep source about as valuable as elephant droppings. Run away. There are enough good prep sources that it doesn't make sense to waste time with junk that will just confuse you. That's my advice.

Let me know if you have any further questions involving these calculations.

Mike