1. **State the problem:** Solve the equation $$\frac{1}{3}x - \frac{2}{3} = \frac{1}{4}x$$. 2. **Identify the least common multiple (LCM) of denominators:** The denominators are 3 and 4. The LCM of 3 and 4 is 12. 3. **Multiply both sides of the equation by 12 to clear fractions:** $$12 \times \left(\frac{1}{3}x - \frac{2}{3}\right) = 12 \times \frac{1}{4}x$$ 4. **Distribute 12 on the left side:** $$12 \times \frac{1}{3}x - 12 \times \frac{2}{3} = 12 \times \frac{1}{4}x$$ 5. **Simplify each term:** $$4x - 8 = 3x$$ 6. **Bring all terms involving $x$ to one side:** $$4x - 3x = 8$$ 7. **Simplify:** $$x = 8$$ **Final answer:** $$x = 8$$