ANSWER
1/12
Step-by-step explanation
There are 36 possible outcomes, 6 for each die. Each outcome is independent.
We have to see which combinations add up to 10. The numbers on each die are {1, 2, 3, 4, 5, 6}.
If we get a 6 on the first die, we need a 4 on the second die. If we get a 5 on the first die, we need a 5 on the second die. If we get a 4 on the first die, we need a 6 in the second.
These are all the combinations that add up to 10: {6-4, 5-5, 4-6}. Thus, from all 36 possible outcomes, there are only 3 in which the dice add up to 10. The odds of getting a sum of 10 are 3/36, or 1/12 (simplifying the fraction).