To solve this expression, we first need to simplify the fractions within the parentheses.

(3 1/6 - 5 1/6: 4 2/15) = (19/6 - 31/6: 62/15)

Next, we perform the division by multiplying the first fraction in the parentheses by the reciprocal of the second fraction:

(19/6 - 31/6) (15/62) = (19/6 - 31/6) (15/62)
= (-12/6) * (15/62)
= -180/372
= -15/31

Now, we multiply this result by 3/92:

(-15/31) * (3/92)
= -45 / 286

Therefore, the simplified answer is -45/286.