To solve this problem, we need to simplify each of the components separately before performing the operations.

For the first part: 12 4/5 3 3/4 - 4 4/11 4 1/8

Convert the mixed numbers into improper fractions:
12 4/5 = 64/5
3 3/4 = 15/4
4 4/11 = 48/11
4 1/8 = 33/8

Calculate the products:
64/5 15/4 = 192/5
48/11 33/8 = 396/11

Subtract the products:
192/5 - 396/11 = (19211 - 3965) / (5 * 11)
= (2112 - 1980) / 55
= 132 / 55

For the second part: 11 2/3 : 2 4/7

Convert the mixed numbers into improper fractions:
11 2/3 = 35/3
2 4/7 = 18/7

Divide the fractions:
35/3 ÷ 18/7 = (35/3) * (7/18)
= 245/54

Finally, the answer is:
(132/55) / (245/54) = (132/55) * (54/245)
= 7128/2675

Therefore, the final result is 7128/2675.