Factor out common terms from the numerator and denominator of the fraction.

The numerator is $12x - 6y$. The common factor is 6.

$$12x - 6y = 6(2x - y)$$

The denominator is $4x - 2y$. The common factor is 2.

$$4x - 2y = 2(2x - y)$$

$$\frac{12x - 6y}{4x - 2y} = \frac{6(2x - y)}{2(2x - y)}$$

Assuming $2x - y \neq 0$, we can cancel the term $(2x - y)$.

$$\frac{6}{2} = 3$$

The original expression is $\frac{12x - 6y}{4x - 2y} + 24x - 9y$.
Substituting the simplified fraction, we get:

$$3 + 24x - 9y$$