Evaluate the numerator following the order of operations (multiplication and division before subtraction).

$$\text{Numerator} = 36 - 8 \times 4 - 15 \div -3$$

First, perform the multiplication:

$$8 \times 4 = 32$$

Next, perform the division:

$$15 \div -3 = -5$$

Substitute these values back into the numerator:

$$\text{Numerator} = 36 - 32 - (-5)$$ $$\text{Numerator} = 36 - 32 + 5$$ $$\text{Numerator} = 4 + 5$$ $$\text{Numerator} = 9$$

$$\text{Denominator} = -3 \times -3 - 8(-6 + 2)$$

First, evaluate the expression inside the parentheses:

$$-6 + 2 = -4$$

Substitute this value back:

$$\text{Denominator} = -3 \times -3 - 8(-4)$$

Next, perform the multiplications:

$$-3 \times -3 = 9$$ $$8 \times -4 = -32$$

Substitute these values back into the denominator:

$$\text{Denominator} = 9 - (-32)$$ $$\text{Denominator} = 9 + 32$$ $$\text{Denominator} = 41$$

$$\frac{\text{Numerator}}{\text{Denominator}} = \frac{9}{41}$$

The evaluated expression is $\frac{9}{41}$.