Lihaan walks $8\text{m}$ towards South from his office to reach the park. Then he takes a left turn and walks $15\text{m}$ to reach a traffic signal. Then he turns $90^{\circ }$ in an anti-clockwise direction and walks $8\text{m}$ to reach a coffee shop. He takes a left turn and walks $8\text{m}$ to reach home. The office is in which direction with respect to Lihaan's home?

Let's trace the path starting from the Office at $(0,0)$:
1. Walks $8\text{m}$ South to Park $⟹$ Coordinates: $(0,-8)$.
2. Turns left (facing East) and walks $15\text{m}$ to traffic signal $⟹$ Coordinates: $(15,-8)$.
3. Turns $90^{\circ }$ anti-clockwise (now facing North) and walks $8\text{m}$ to coffee shop $⟹$ Coordinates: $(15,0)$.
4. Takes a left turn (now facing West) and walks $8\text{m}$ to reach home $⟹$ Coordinates: $(15-8,0)=(7,0)$.
Now, we find the direction of the Office $(0,0)$ with respect to Home $(7,0)$:
Since the office lies on the same horizontal line but to the left of the home, it is due West.