To solve this equation, we first need to convert the mixed numbers into improper fractions.

4 8/15 = (415 + 8)/15 = 68/15
1 1/3 = (13 + 1)/3 = 4/3
1 7/8 = (1*8 + 7)/8 = 15/8

Now, we can substitute these values back into the equation:

(68/15 - 4/3) * 15/8

Now, we simplify each step:

68/15 = 272/60
4/3 = 80/60
15/8 = 112/60

(272/60 - 80/60) 112/60
192/60 112/60
(192112) / (6060)
21504 / 3600

Therefore, (4 8/15 - 1 1/3) * 1 7/8 = 21504 / 3600 = 59.7333