2 7/16 - (2 3/8 - 1 2/3) + 2 7/12

First, we need to simplify the expression inside the parentheses:

2 3/8 - 1 2/3 = (19/8) - (5/3)
Convert fractions into a common denominator:
= (57/24) - (40/24)
= 17/24

Now, substitute this back into the original expression:

2 7/16 - 17/24 + 2 7/12
Convert all fractions into a common denominator (48):
(77/48) - (34/48) + (95/48)
= 138/48
= 2 39/48

Therefore, the result of the expression is 2 39/48.