Rest assured as you have done nothing wrong. Essentially, N, N ethylmethylethanamine is absolutely the same as N Ethyl, N methylethanamine. There can definitely be different IUPAC names for the same compound and you have stumbled across one of the same example. So don't worry as the examiner who will be checking your copy will receive the guideline regarding one more correct version of the answer, which is the same as yours.

Hope I have answered your question. All the best!