1. **Stating the problem:** We are given two displacement vectors for a drone's journey: $\overrightarrow{AB} = (4,8,6)$ km and $\overrightarrow{BC} = (-1,-4,6)$ km. We need to find the total displacement vector $\overrightarrow{AC}$ from point A to C. 2. **Formula used:** The total displacement vector from A to C is the vector sum: $$\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC}$$ 3. **Calculation:** $$\overrightarrow{AC} = (4,8,6) + (-1,-4,6) = (4 + (-1), 8 + (-4), 6 + 6)$$ $$\overrightarrow{AC} = (3, 4, 12)$$ 4. **Explanation:** Adding vectors means adding their corresponding components. Here, the x-components add to 3, y-components to 4, and z-components to 12. **Final answer:** $$\boxed{\overrightarrow{AC} = (3, 4, 12)}$$