Solution:

The answer is (D). Suppose first that $n$ is even: then it is not a multiple of 3, because one of Alessandro's two statements must be false, and hence (using what Daniele says) the units digit of $n$ must be 5, but this is impossible for an even number. The number $n$ (if it exists) is therefore a multiple of 3: Alessandro's first statement is then false, so $n$ is odd, and by what Daniele says the units digit cannot be 5. Hence $n$ cannot be a multiple of 5, because its units digit (which cannot be 0, since $n$ is odd) would be 5: it follows that the true statement made by Manuela is that the sum of the digits is 12. The only two-digit numbers whose digits sum to 12 are $39, 48, 57, 66, 75, 84$ and $93$, and among these we must take only those that are odd and multiples of 3, which are $39, 57$ and $93$.