X walks $3\text{km}$ away from his starting point. He turns right and travels a further $8\text{km}$. He turns left and walks ahead, but notices that he is in the opposite direction of what he is supposed to be in. He started by walking towards east. In which direction is he supposed to go?

Let's follow the movements based on the initial direction being East:
1. Starts walking East for $3\text{km}$.
2. Turns Right, which means he is now facing South ($8\text{km}$).
3. Turns Left, which means he is now facing East again.
4. At this point, he realizes he is moving in the opposite direction of where he is supposed to go. Since he is currently walking East, the opposite direction is West.
Hence, he is supposed to go towards the West.