Kailash walks $3\text{km}$ to East and turns South and walks $4\text{km}$. Again turns West and walks $6\text{km}$. How far is he from the starting point?

Let us trace the path coordinates from a starting point $(0,0)$:
1. Walks $3\text{km}$ East $\to (3,0)$
2. Turns South and walks $4\text{km}$ $\to (3,-4)$
3. Turns West and walks $6\text{km}$ $\to (3-6,-4)=(-3,-4)$

Now, find the net distance from the starting point $(0,0)$ to the final point $(-3,-4)$ using the distance formula / Pythagoras' theorem:

$$\text{Distance}=\sqrt{(-3-0{)}^2+(-4-0{)}^2}=\sqrt{(-3{)}^2+(-4{)}^2}$$

$$\text{Distance}=\sqrt{9+16}=\sqrt{25}=5\text{km}$$