Akul walks $4\text{kilometres}$ towards East and then he turns South and walks $14\text{kilometres}$. Then he turns East and walks $7\text{kilometres}$. In which direction is Akul now from his starting point?

Let's trace Akul's movement using cartesian coordinates, with the starting point at $(0,0)$:
1. Starts at $(0,0)$.
2. Walks $4\text{km}$ East $\to$ Position is $(4,0)$.
3. Turns South and walks $14\text{km}$ $\to$ Position is $(4,-14)$.
4. Turns East and walks $7\text{km}$ $\to$ Final position is $(4+7,-14)=(11,-14)$.

The final coordinates $(11,-14)$ correspond to the East direction (+x) and South direction (-y).
Therefore, Akul is in the South-East direction relative to his starting point.