Some people will try to convince you that one is the loneliest number, that 4 for 4 is better than 1 for 1, and that 2 + 2 = 3. In what situation would the following calculations be considered correct?

9 + 5 = 2
12 + 3 = 3
10 + 6 = 4

Here is the SOLUTION.

THE SOLUTION:

Any base-12 system that repeats may fit this pattern (as some readers reveal in the comments); my answer deals with time.

9 + 5 = 2 Take 9 o'clock, add five hours, and it's 2 o'clock.
12 + 3 = 3 Take 12 o'clock, and three hours later, it's 3 o'clock.
10 + 6 = 4 From 10 o'clock, six hours later it would be 4 o'clock.