1. **State the problem:** Simplify the expression $$\frac{x^2 - 36}{x + 4} \cdot \frac{4x}{6x - 36}$$. 2. **Recall important formulas and rules:** - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$. - Factor common terms in numerator and denominator. - Simplify by canceling common factors. 3. **Factor each part:** - $$x^2 - 36 = (x - 6)(x + 6)$$ (difference of squares). - $$6x - 36 = 6(x - 6)$$ (factor out 6). 4. **Rewrite the expression with factored terms:** $$\frac{(x - 6)(x + 6)}{x + 4} \cdot \frac{4x}{6(x - 6)}$$ 5. **Combine the fractions:** $$\frac{(x - 6)(x + 6) \cdot 4x}{(x + 4) \cdot 6(x - 6)}$$ 6. **Cancel common factors:** - Cancel $$x - 6$$ from numerator and denominator. 7. **Simplify the expression:** $$\frac{(x + 6) \cdot 4x}{(x + 4) \cdot 6} = \frac{4x(x + 6)}{6(x + 4)}$$ 8. **Reduce the fraction $$\frac{4}{6}$$ to $$\frac{2}{3}$$:** $$\frac{2x(x + 6)}{3(x + 4)}$$ **Final simplified expression:** $$\frac{2x(x + 6)}{3(x + 4)}$$