3/4 + 2 2/5 * 2 1/2 - 3 5/6

First, we need to simplify the multiplication and division before addition and subtraction:

2 2/5 2 1/2
= (12/5) (5/2)
= 12/1
= 12

Now we can plug back in the result into the original expression:

3/4 + 12 - 3 5/6
= 3/4 + 12 - 3 5/6
= 3/4 + 12 - (4 + 5/6)
= 3/4 + 12 - 4 - 5/6
= 3/4 + 12 - 4 - 5/6
= 3/4 + 12-4 - 5/6
= 3/4 + 8 - 5/6
= 3/4 + 8 - 5/6
= 8 3/4 - 5/6
= 8 18/24 - 20/24
= 8 18/24 - 20/24
= 8 18/24 - 20/24
= 7 22/24
= 7 11/12.

So, 3/4 + 2 2/5 * 2 1/2 - 3 5/6 = 7 11/12.