1. **State the problem:** Solve the inequality $$\frac{x}{4} > 8$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator to eliminate the fraction. Since 4 is positive, the inequality direction remains the same. 3. **Intermediate work:** $$\frac{x}{4} > 8$$ Multiply both sides by 4: $$\cancel{4} \times \frac{x}{\cancel{4}} > 8 \times 4$$ Simplifies to: $$x > 32$$ 4. **Explanation:** Multiplying both sides by 4 removes the denominator. Because 4 is positive, the inequality sign does not flip. The solution is all values of $x$ greater than 32. **Final answer:** $$x > 32$$