1. **State the problem:** We are given the ratio of students who preferred athletics, rugby, and baseball as 15 : 6 : 4. 2. **Find the total parts in the ratio:** Add the parts of the ratio together: $$15 + 6 + 4 = 25$$ 3. **Calculate the percentage of students who preferred rugby:** The number of parts for rugby is 6. To find the percentage, use the formula: $$\text{Percentage} = \left(\frac{\text{Part for rugby}}{\text{Total parts}}\right) \times 100$$ Substitute the values: $$\text{Percentage} = \left(\frac{6}{25}\right) \times 100$$ 4. **Simplify the fraction:** $$\text{Percentage} = \left(\frac{\cancel{6}}{\cancel{25}}\right) \times 100 = 24\%$$ 5. **Final answer:** 24% of the students preferred rugby.