To solve this expression, we'll first simplify the terms within the parentheses and then perform the division and multiplication.

Given expression: 4/3 ÷ (5/6 + 0.25) - 3.6 × (7/12 + 1/9)

Step 1: Simplify the terms within the parentheses.
5/6 + 0.25 = 5/6 + 1/4 = (10/12) + (3/12) = 13/12

7/12 + 1/9 = 7/12 + 4/36 = 7/12 + 1/9 = (21/36) + (4/36) = 25/36

Step 2: Perform the division and multiplication.
4/3 ÷ 13/12 - 3.6 × 25/36

To divide fractions, we multiply by the reciprocal:
4/3 × 12/13 = 16/13

Now the expression becomes:
16/13 - 3.6 × 25/36

To multiply fractions, we multiply straight across:
3.6 × 25 = 90

The expression becomes:
16/13 - 90/36

To subtract fractions, we need a common denominator:
16/13 - 90/36 = (1636)/(1336) - 90/36 = 576/468 - 90/36

Now subtract the fractions:
576/468 - 90/36 = 576/468 - 90/36 = 124/468 - 90/36 = 34/468 = 17/234

Therefore, the simplified answer is 17/234.