A man started walking towards south. After moving 4 km he turned towards east and walked 6 km. Again he turned towards north and walked 12 km. How far is he from the starting point?

Let us trace the path step-by-step from the origin $(0,0)$:
1. Walks 4 km South: Position is $(0,-4)$.
2. Turns East and walks 6 km: Position is $(6,-4)$.
3. Turns North and walks 12 km: Position is $(6,-4+12)=(6,8)$.

To find the straight-line distance from the starting point $(0,0)$ to the final position $(6,8)$, we apply the Pythagorean theorem:

$$\text{Distance}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ km}$$