V-기 쉽다
This pattern means that something is easy to happen or likely to happen, often with a sense of risk or tendency. In the story, "방향을 잃기 쉬웠다" means the fog made it easy to lose direction. You can reuse it in many situations, for example: "비가 오면 길을 잃기 쉽다." It means "When it rains, it is easy to lose the way."
비가 오면 길을 잃기 쉽다.
When it rains, it is easy to lose the way.
