1. **State the problem:** We know the winner receives half (\(\frac{1}{2}\)) of the total prize money and gets N6,000. 2. **Define variables:** Let \(T\) be the total prize money distributed. 3. **Set up the equation for the winner's prize:** The winner's prize is half of \(T\): $$\frac{1}{2} T = 6000$$ 4. **Solve for the total prize money \(T\):** Multiply both sides by 2: $$T = 6000 \times 2 = 12000$$ 5. **Find the second runner up's prize:** Second runner up receives \(\frac{1}{4}\) of the winner's prize: $$\frac{1}{4} \times 6000 = 1500$$ 6. **Verify total distribution assumption:** The question is about total prize money, and since the winner's prize is half, and the second runner up gets a quarter of the winner's prize, the total prize money \(T\) is N12,000. **Final answer: N12,000**