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