1. **Stating the problem:** We are given a segment $\overline{BD} = 12$ cm and points $A, B, C, D, O$ on a figure. We need to find the length $\overline{BO}$. 2. **Understanding the problem:** Without additional information about the figure (such as whether $O$ is the midpoint of $\overline{BD}$, or any other relationships), we cannot directly calculate $\overline{BO}$. 3. **Assuming $O$ is the midpoint of $\overline{BD}$:** This is a common scenario in geometry problems. 4. **Formula for midpoint:** If $O$ is the midpoint of $\overline{BD}$, then $$\overline{BO} = \overline{OD} = \frac{\overline{BD}}{2}$$ 5. **Calculate $\overline{BO}$:** $$\overline{BO} = \frac{12}{2} = 6$$ 6. **Conclusion:** The length $\overline{BO}$ is 6 cm under the assumption that $O$ is the midpoint of $\overline{BD}$.