1. **State the problem:** Simplify the expression $$\frac{(3x-4)(7x-3)}{(7x-3)(x+6)} \cdot \frac{(x+6)}{(3x-4)}$$. 2. **Recall the rule:** When multiplying fractions, multiply numerators together and denominators together. 3. **Write the full expression as a single fraction:** $$\frac{(3x-4)(7x-3) \cdot (x+6)}{(7x-3)(x+6) \cdot (3x-4)}$$ 4. **Look for common factors in numerator and denominator:** - $(3x-4)$ appears in numerator and denominator. - $(7x-3)$ appears in numerator and denominator. - $(x+6)$ appears in numerator and denominator. 5. **Cancel all common factors:** $$\frac{\cancel{(3x-4)} \cdot \cancel{(7x-3)} \cdot \cancel{(x+6)}}{\cancel{(7x-3)} \cdot \cancel{(x+6)} \cdot \cancel{(3x-4)}} = 1$$ 6. **Final answer:** The expression simplifies to **1**. This means the entire expression reduces to 1 for all values of $x$ where the original expression is defined (i.e., where denominators are not zero).