1. **State the problem:** Simplify the expression $$\frac{7(2v + 3)(v + 7)}{28(v - 4)(2v + 3)}$$. 2. **Identify common factors:** Notice that both numerator and denominator contain the factor $(2v + 3)$. 3. **Cancel common factors:** We can cancel $(2v + 3)$ from numerator and denominator: $$\frac{7\cancel{(2v + 3)}(v + 7)}{28(v - 4)\cancel{(2v + 3)}}$$ 4. **Simplify constants:** $7$ and $28$ share a common factor of $7$: $$\frac{\cancel{7}(v + 7)}{\cancel{28}(v - 4)} = \frac{1 \cdot (v + 7)}{4 \cdot (v - 4)} = \frac{v + 7}{4(v - 4)}$$ 5. **Final answer:** The simplified expression is $$\boxed{\frac{v + 7}{4(v - 4)}}$$