To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the expression within the parentheses:

5/2 - 1/3 = (15/6) - (2/6) = 13/6

Now, let's substitute this value back into the expression:

(13/6) * 9/2 - 6/7

To multiply fractions, we multiply the numerators together and the denominators together:

(13 * 9) / (6 * 2) - 6/7

= 117/12 - 6/7

To subtract fractions, we need to have a common denominator. The least common multiple of 12 and 7 is 84.

So, let's convert the fractions to have a denominator of 84:

(117/12) * (7/7) = 819/84

(6/7) * (12/12) = 72/84

Now, we can subtract the fractions:

819/84 - 72/84 = (819 - 72) / 84 = 747/84

Finally, we can simplify the fraction:

747/84 = 83/9

Therefore, the expression (5/2 - 1/3) * 9/2 - 6/7 simplifies to 83/9.