The correct answer is 47/6 or 7 5/6
To find this we need to first make them improper fractions instead of mixed numbers. You can do this by multiplying the whole number by the bottom (denominator) and adding it to the top (numberator). Then putting it over the bottom again. He's this in action:
-2 1/3
3*2 + 1 = 7
-7/3
So the first term is actually -7/3. Lets do the same for the second.
-10 1/6
6*10 + 1 = 61
-61/10
Now that we have these, we can give them common denominators and complete the action.
-7/3 - (-61/6)
-14/6 + 61/6
47/6 or 7 5/6