After walking $4\text{km}$, X turned to the right and then walked $3\text{km}$. After that he turned to the left and walked $5\text{km}$. In the end, he was moving towards the north. From which direction did he start the journey?

Let's work backwards from his final direction:
1. In the end, he was moving towards the North. Before this, he had turned left. A left turn resulting in a North heading means his previous direction was East.
2. Before facing East, he had walked $3\text{km}$ after making a right turn. A right turn resulting in an East heading means his original direction was North.
3. Therefore, his initial movement during the first $4\text{km}$ segment was straight towards the North.

Thus, he started his journey heading towards the North.