2 2/3(2 1/3 + 2 5/12) - 4 4/5

First, we need to simplify the terms inside the parentheses:
2 1/3 = 7/3
2 5/12 = 29/12

Adding them together:
7/3 + 29/12
= (47)/(43) + 29/12
= 28/12 + 29/12
= (28 + 29)/12
= 57/12
= 4 9/12
= 4 3/4

Now we can substitute back into the original equation:
2 2/3 (4 3/4) - 4 4/5
= 8/3 19/4 - 24/5
= (819)/(34) - 24/5
= 152/12 - 24/5
= 152/12 - (2412)/(512)
= 152/12 - 288/12
= (152 - 288)/12
= -136/12
= -11 1/3

Therefore, 2 2/3(2 1/3 + 2 5/12) - 4 4/5 equals -11 1/3.