To solve this you need to find the greatest common factor, which in this case is 6. But FIRST change 1 5/6 into 11/6. Then change 1/3 into 2/6. At this point you have 11/6 - 2/6.
Then, subtract the numerators, so 11-2=9. Then you end up with 9/6. Finally, you have to simplify the fraction to simplest form. You can think of a fraction as a division problem (Numerator divided by denominator) so in this case, 9 divided by 6, which is 1 1/3. Therefore, your final answer is 1 1/3