Seema ran $8\text{ km}$ towards east, then turned left and walked $6\text{ km}$, then she turned right and walked for $4\text{ km}$. Finally, she took a right turn and walked for $18\text{ km}$ and reached her home. In which direction is her home located with respect to the starting point?

Let's trace the path starting from $O(0,0)$:
1. Moves $8\text{ km}$ East $⟹$ reaches $(8,0)$.
2. Turns left (North) and walks $6\text{ km}$ $⟹$ reaches $(8,6)$.
3. Turns right (East) and walks $4\text{ km}$ $⟹$ reaches $(8+4,6)=(12,6)$.
4. Turns right (South) and walks $18\text{ km}$ $⟹$ reaches $(12,6-18)=(12,-12)$.

The final coordinates of her home are $(12,-12)$. Since the $x$ -coordinate is positive (East) and the $y$ -coordinate is negative (South), the position lies in the South-East quadrant with respect to the origin $(0,0)$.