If one thing hinges on another, the first thing depends on the second thing or is very influenced by it.

The prosecution's case hinged on the evidence of a witness who died before the trial. 控方的案子取决于一位证人的证词，而该证人已在审判前死去。

If a story or situation hinges on an idea or subject, it develops from that idea or that is the most important subject in it.

The film's plot hinges on a case of mistaken identity. 该电影的情节围绕着一宗身份误认案展开。