1. **State the problem:** Simplify the expression $$3(4u^2 - 1)$$. 2. **Formula and rules:** Use the distributive property, which states that $$a(b + c) = ab + ac$$. Here, multiply 3 by each term inside the parentheses. 3. **Apply the distributive property:** $$3(4u^2 - 1) = 3 \times 4u^2 - 3 \times 1$$ 4. **Calculate each term:** $$= 12u^2 - 3$$ 5. **Final answer:** The simplified expression is $$12u^2 - 3$$.