A man walks 2 km towards East and then he turns to South and walks 6 km. Again he turns to East and walks 4 km, after this he turns to North and walk 14 km. How far is he from his starting point?

The correct option is 10 km.

Let us break down the man's movement step-by-step to find his final position relative to the starting point. Let the starting point be represented as the origin $(0,0)$ on a standard coordinate plane where East is along the positive x-axis, North is along the positive y-axis, West is along the negative x-axis, and South is along the negative y-axis.

Step 1: Walk 2 km East
Starting from $(0,0)$, walking 2 km East brings him to:
$P_1=(2,0)$

Step 2: Turn South and walk 6 km
From $(2,0)$, walking 6 km South (towards the negative y-direction) brings him to:
$P_2=(2,0-6)=(2,-6)$

Step 3: Turn East and walk 4 km
From $(2,-6)$, walking 4 km East (towards the positive x-direction) brings him to:
$P_3=(2+4,-6)=(6,-6)$

Step 4: Turn North and walk 14 km
From $(6,-6)$, walking 14 km North (towards the positive y-direction) brings him to his final position:
$P_4=(6,-6+14)=(6,8)$

Step 5: Calculate the distance from the starting point
To find how far he is from his starting point $(0,0)$, we use the distance formula:
$\text{Distance}=\sqrt{{(6-0)}^2+{(8-0)}^2}$
$\text{Distance}=\sqrt{6^2+8^2}$
$\text{Distance}=\sqrt{36+64}$
$\text{Distance}=\sqrt{100}=10\text{km}$

Therefore, the man is 10 km away from his starting point.