5 odd sums are possible.
Explanation:
Since there are two dices and each has 6 sides, the highest possible sum is 12. The lowest possible sum is 2, because 1 + 1 = 2 and there can't be 0 + 0 or 0 + 1. That leaves us with: 2,3,4,5,6,7,8,9,10,11,12. Out of those numbers, 5 are odd (3,5,7,9,11). Therefore, 5 odd sums are possible
