1. **State the problem:** Ethan is thinking of a negative number that is lower than $-4$ and higher than $-10$. The number is odd and a multiple of 3. 2. **Identify the range:** The number must satisfy $$-10 < x < -4$$ where $x$ is an integer. 3. **List integers in the range:** The integers between $-10$ and $-4$ are $$-9, -8, -7, -6, -5$$. 4. **Check for odd numbers:** Among these, the odd numbers are $$-9, -7, -5$$. 5. **Check for multiples of 3:** A number is a multiple of 3 if it can be written as $$3k$$ where $k$ is an integer. - $-9 = 3 \times (-3)$, so it is a multiple of 3. - $-7$ is not divisible by 3. - $-5$ is not divisible by 3. 6. **Conclusion:** The number Ethan is thinking of is $$\boxed{-9}$$ because it is the only number in the range that is both odd and a multiple of 3.