First, let's simplify the expression inside the parentheses before multiplying by 4 2/7.

3 x (2 x 5 5/6 - 15.4) = 3 x (10 5/6 - 15.4)
= 3 x (10 + 5/6 - 15.4)
= 3 x (10 + 5/6 - 92/5)
= 3 x (10 + 5/6 - 92/5)
= 3 x (60/6 + 5/6 - 92/6)
= 3 x (-27/6)
= -81/6
= -13.5

Now, multiply -13.5 by 4 2/7:

-13.5 x 4 2/7 = -13.5 x 30/7
= (-135/10) x 30/7
= -405/70
= -5.7857

Therefore, the final result is -5.7857.