To solve this expression, we need to simplify each part of the expression separately and then combine the results.

First, let's simplify each part:

3 - 1/4 + 2/3 = (9/3) - (1/4) + (8/12) = 27/12 - 3/12 + 8/12 = 32/12 = 8/3

5 - 1/3 - 6/5 = (25/5) - (1/3) - (18/5) = 25/5 - 5/15 - 18/5 = 25/5 - 1/3 - 18/5 = 15/3 - 1/3 - 18/5 = 14/3 - 18/5 = (70/15) - (54/15) = 16/15

6 - 7/4 - 3/2 = (24/4) - (7/4) - (6/2) = 24/4 - 7/4 - 6/2 = 17/4 - 6/2 = 17/4 - 12/4 = 5/4

Now, let's substitute these simplified values back into the original expression:

(8/3) - (16/15) - (5/4) = (40/15) - (16/15) - (75/60) = 40/15 - 16/15 - 75/60 = 24/15 - 75/60 = (96/60) - (75/60) = 21/60 = 7/20

Therefore, the simplified expression is 7/20.