1. **State the problem:** Simplify the expression using the distributive property: $$\frac{1}{4}(12 + 16v)$$ 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $$a(b + c) = ab + ac$$ 3. **Apply the distributive property:** Multiply $$\frac{1}{4}$$ by each term inside the parentheses: $$\frac{1}{4} \times 12 + \frac{1}{4} \times 16v$$ 4. **Calculate each multiplication:** $$\frac{12}{4} + \frac{16v}{4}$$ 5. **Simplify the fractions:** $$\cancel{\frac{12}{4}}3 + \cancel{\frac{16v}{4}}4v$$ 6. **Write the final simplified expression:** $$3 + 4v$$