1. **State the problem:** Solve the equation $$\frac{x}{3} - \frac{x}{6} = 4$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combine terms easily. 3. **Find common denominator:** The denominators are 3 and 6. The least common denominator (LCD) is 6. 4. **Rewrite fractions with LCD:** $$\frac{x}{3} = \frac{2x}{6}$$ 5. **Substitute back:** $$\frac{2x}{6} - \frac{x}{6} = 4$$ 6. **Combine fractions:** $$\frac{2x - x}{6} = 4$$ $$\frac{x}{6} = 4$$ 7. **Isolate $x$ by multiplying both sides by 6:** $$\cancel{6} \times \frac{x}{\cancel{6}} = 4 \times 6$$ $$x = 24$$ 8. **Final answer:** $$x = 24$$