The mistake the student made is:
The numbering should be 1,2 (smallest number)
In the case of naming 2,3-dimethylcyclohexane, the correct way to number the positions for substituents in a cyclohexane ring is to start at one of the substituents and assign numbers to each carbon in such a way that the substituents receive the lowest possible numbers. Thus, the correct numbering would minimize the larger number assigned to substituents, which in this case would likely yield 1 and 2 as the positions for the two methyl groups instead of 2 and 3.