1. **State the problem:** Simplify the expression $$\frac{3 - x}{6} - \frac{2x}{9}$$. 2. **Find a common denominator:** The denominators are 6 and 9. The least common denominator (LCD) is 18. 3. **Rewrite each fraction with the LCD:** $$\frac{3 - x}{6} = \frac{(3 - x) \times 3}{6 \times 3} = \frac{3(3 - x)}{18} = \frac{9 - 3x}{18}$$ $$\frac{2x}{9} = \frac{2x \times 2}{9 \times 2} = \frac{4x}{18}$$ 4. **Subtract the fractions:** $$\frac{9 - 3x}{18} - \frac{4x}{18} = \frac{9 - 3x - 4x}{18} = \frac{9 - 7x}{18}$$ 5. **Final answer:** $$\boxed{\frac{9 - 7x}{18}}$$ This is the simplified form of the given expression.