The rational number -4 can be represented in various ways, and we need to identify which of the given responses correctly represents -4 as a rational number.
1. **14**: This is not equal to -4.
2. **Start Fraction 1 over 4 End Fraction** (which means \( \frac{1}{4} \)): This is a positive number and does not equal -4.
3. **−12√3**: This is not a rational number (since it involves a square root).
4. **Start Fraction negative square root of 12 over 3 End Fraction** (which means \( \frac{-\sqrt{12}}{3} \)): This simplifies to \( \frac{-2\sqrt{3}}{3} \) and is not equal to -4.
5. **−246 Startfraction negative 24 over 6 End Fraction** (which means \( -\frac{24}{6} \)): This simplifies to -4, which is equal to -4.
6. **144√3**: This is a positive number and does not equal -4.
The response that correctly represents -4 as a rational number is:
**−246 Startfraction negative 24 over 6 End Fraction** (which is \( -4 \)).