Which one of the following poses a great danger?

Leaking fuel lines pose a significant danger because they can lead to fuel spills that create fire hazards or even explosions on a boat. Fuel is highly flammable, and any escaping fuel can easily ignite if it comes into contact with a spark or open flame. This not only endangers those on board but also poses risks to other vessels in the vicinity and the environment.

In contrast, storage of life jackets is important for safety but does not pose an immediate danger if done correctly. Using new cleaning solutions carries risks, but these are typically related to chemical exposure rather than immediate physical danger. Detailed engine inspections are crucial for ensuring the safe operation of a boat and, when performed correctly, actually help mitigate the risk of accidents. Thus, while all the options involve safety considerations, leaking fuel lines represent the most immediate and severe risk.