To solve this expression, we first need to convert the mixed numbers to improper fractions:

3 1/6 = (36+1)/6 = 19/6
5 1/6 = (56+1)/6 = 31/6
4 2/15 = (4*15+2)/15 = 62/15

Now we can substitute these values back into the expression:

(19/6 + 31/6) / (62/15) 3/92
= (50/6) / (62/15) 3/92
= (25/3) (15/31) 3/92
= 375/93 * 3/92
= 1125/2796

Therefore, the final result is 1125/2796.