1. **State the problem:** Simplify the expression $$\frac{\frac{x^2+4x}{3y}}{\frac{x^2-16}{12y^2}}$$. 2. **Rewrite the division of fractions as multiplication:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{\frac{x^2+4x}{3y}}{\frac{x^2-16}{12y^2}} = \frac{x^2+4x}{3y} \times \frac{12y^2}{x^2-16}$$. 3. **Factor expressions where possible:** - Factor numerator $x^2+4x$ as $x(x+4)$. - Factor denominator $x^2-16$ as $(x-4)(x+4)$ (difference of squares). So the expression becomes: $$\frac{x(x+4)}{3y} \times \frac{12y^2}{(x-4)(x+4)}$$. 4. **Multiply numerators and denominators:** $$\frac{x(x+4) \times 12y^2}{3y \times (x-4)(x+4)}$$. 5. **Simplify common factors:** - Cancel $(x+4)$ from numerator and denominator. - Simplify $\frac{12y^2}{3y} = 4y$. The expression reduces to: $$\frac{x \times 4y}{x-4} = \frac{4xy}{x-4}$$. 6. **Final answer:** $$\boxed{\frac{4xy}{x-4}}$$. This is the simplified form of the original expression.