To subtract fractions with different denominators, we need to first find a common denominator. In this case, the least common multiple of 6 and 9 is 18.
Converting 1 2/9 to an improper fraction, we get:
1 2/9 = 9/9 + 2/9 = 11/9
So, we have:
1 2/9 - 5/6 = 11/9 - 10/18
Now, we can subtract the fractions by finding a common denominator:
11/9 - 10/18 = (22/18) * (11/9) - (1/1) * (10/18)
= 22/18 - 10/18
= 12/18
Simplifying 12/18 by dividing the numerator and denominator by their greatest common factor, which is 6, we get:
12/18 = 2/3
Therefore, 1 2/9 - 5/6 = 2/3.