To add and subtract mixed numbers and fractions, you must first convert the mixed numbers to improper fractions.

4/5 = 20/5 = 4
2/3 = 2/3
3:3/4 = 9/4
1/6 = 1/6
1/15 = 1/15

Now, perform the operations:

4 - 2/3 = 12/3 - 2/3 = 10/3

10/3 - 9/4 = (40/12) - (27/12) = 13/12

13/12 - 1/6 = (78/72) - (12/72) = 66/72 = 11/12

11/12 - 1/15 = (165/180) - (12/180) = 153/180 = 17/20

Therefore, 4/5 - 2/3 - 3:3/4 - 1/6 - 1/15 = 17/20