It's neither. If it were to be an improper fraction, it would be something like 3/2 instead of 2/3. If it were to be a mixed number, it would look like 1 1/3.
In order for a fraction to be improper, the numerator must be greater than the denominator. In order for a fraction to be a mixed number, there must be a whole number and a fraction.
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<u><em /></u><em>The fraction 2 over 3 is </em> not an improper fraction, nor is it a mixed number.