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The largest digits number with only 2 digits alike is 99
99
45. There are only 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. So I am not sure where the "99 digits", in the question come from.
99 Or how about (9)9 ?
This question can be answered regardless of what digits are used. If there are four options for the first digit, then there are only 3 options for the second digit, and 2 options for the third. There are no options left for the fourth and final digit. So, the answer is 4! (or four factorial).