The problem asks for the length of segment $CD$, given that $DE = 6$ and $CE = 15$.

To find $CD$, you can use the fact that $CE = CD + DE$. We can express this as:

$CE = CD + DE$

Substituting the given values:

$15 = CD + 6$

Now, solve for $CD$:

$CD = 15 - 6 = 9$

Thus, the length of segment $CD$ is $9$.

Would you like more details or have any questions? Here are five related questions to further explore:

1. If $DE$ was 7 instead of 6, what would $CD$ be?
2. How would the calculation change if $CE$ was 20 and $DE$ remained 6?
3. Can you find the value of $CE$ if $CD = 10$ and $DE = 5$?
4. What is the relationship between the lengths of segments $CD$ and $DE$?
5. How would you express $CD$ in terms of $CE$ and $DE$?

Tip: When solving problems involving segments, always verify that the sum of smaller segments equals the total segment length to ensure your calculations are correct.