1. **State the problem:** Solve the inequality $\frac{x}{3} > 4$. 2. **Formula and rules:** To solve inequalities involving division or multiplication by a positive number, you can multiply or divide both sides by that number without changing the inequality direction. 3. **Step-by-step solution:** Multiply both sides by 3 (which is positive): $$\frac{x}{3} \times 3 > 4 \times 3$$ Simplifies to: $$x > 12$$ 4. **Interpretation:** The solution means all values of $x$ greater than 12 satisfy the inequality. **Final answer:** $$x > 12$$