To simplify the expression, we will first convert all the mixed numbers to improper fractions.

4 1/8 = (84 + 1) / 8 = 33/8
2 1/4 = (42 + 1) / 4 = 9/4
1 1/7 = (7*1 + 1) / 7 = 8/7

Now we can rewrite the expression and perform the necessary operations:

(33/8 6/11) / (9/4) / (8/7 3/4) / 3/10
= (33/8 6/11) / (9/4) / (8/7 3/4) / (3/10)
= (336 / 811) / (9/4) / (83 / 74) / (3/10)
= (198 / 88) / (9/4) / (24 / 28) / (3/10)
= (198 / 88) (4/9) (28/24) (10/3)
= (9/11) (28/24) (10/3)
= (9/11) (7/6) * (10/3)
= 630 / 198
= 35/11

Therefore, the simplified result of the given expression is 35/11.