1. **Problem statement:** In right triangle ABC, altitude CD is drawn to the hypotenuse AB. Given that the altitude CD has length 6 and segment AD has length 12, find the length of segment DB. 2. **Relevant formula:** When an altitude is drawn to the hypotenuse of a right triangle, it creates two smaller right triangles that are similar to the original triangle and to each other. A key property is: $$CD^2 = AD \times DB$$ This means the square of the altitude equals the product of the two segments into which the hypotenuse is divided. 3. **Apply the formula:** Substitute the known values: $$6^2 = 12 \times DB$$ $$36 = 12 \times DB$$ 4. **Solve for DB:** $$DB = \frac{36}{12} = 3$$ 5. **Answer:** The length of DB is 3. Therefore, the correct choice is B. 3.