To solve this expression, we follow the order of operations:

First, simplify the multiplication:
(-3.8 + 2 1/3) = (-3.8 + 2) + 1/3 = -1.8 + 1/3 = -1 17/30

Next, simplify the division:
4 1/6 ÷ (-1 2/3) = 25/6 ÷ (-5/3) = 25/6 × (-3/5) = -75/30 = -2 1/2

Now, perform the final subtraction on the multiplication result and the division result:
(-1 17/30) × (-1 7/8) + (-2 1/2) = (-1 17/30) × (-15/8) + (-2 1/2)
= (529/30) × (-15/8) + (-5/2)
= (-7945/120) + (-60/120)
= (-8005/120)
= -66 41/120

Therefore, the final result of the expression is -66 41/120.