A man walks $20\text{ m}$ towards north, then he turns right and walks $3\text{ m}$, then turns left and walks $4\text{ m}$ and from there he walks $4\text{ m}$ towards east. How far and in which direction is he from his initial position?

Let's follow the steps mathematically from origin $(0,0)$:Walks $20\text{ m}$ North $⟹(0,20)$ Turns right (East) and walks $3\text{ m}⟹(3,20)$ Turns left (North) and walks $4\text{ m}⟹(3,24)$ Walks $4\text{ m}$ East $⟹(3+4,24)=(7,24)$ Now calculate the straight line distance from $(0,0)$ to $(7,24)$ using the Pythagorean theorem:
$$\text{Distance}=\sqrt{7^2+24^2}=\sqrt{49+576}=\sqrt{625}=25\text{ m}$$
Since both coordinates are positive $(+x,+y)$, his direction relative to the start point is North-East.