To solve this expression, we will follow the order of operations (PEMDAS):

First, let's simplify the expression within the parentheses:
71/15 - 19/12 = (7112 - 1519) / (15*12) = (852 - 285) / 180 = 567 / 180 = 63 / 20

Substitute the simplified expression back into the original expression:
0.9 * 11/12 - (63/20) / 84/10

Next, simplify the division within the parentheses:
(63/20) / (84/10) = (63/20) (10/84) = (6310) / (20*84) = 630 / 168 = 315 / 84 = 45 / 12 = 15 / 4

Substitute back into the original expression:
0.9 * 11/12 - 15/4

Now, simplify the multiplication and subtraction:
= (0.9 * 11)/12 - (15/4) = 9.9/12 - 15/4
= 0.825 - 3.75
= -2.925

Therefore, the final answer is -2.925.