One way to hold amenable is to picture something that can be led. Not pushed, not forced — led, the way you lead a horse by walking in front of it. If a person can be led toward your suggestion, they are amenable. If a problem can be led into shape by a particular method, that problem is amenable to it. And if someone can be led in front of a judge, they are amenable to that court. In every case the question is the same: is there a way in, a handle by which this can be brought along?
From the word’s history
The supplied source derives amenable from Anglo-Norman amenable, from amener, to bring or lead in, which is a- plus mener, to lead. The modern uses all keep that leading picture, which is why one adjective can cover a willing person, a treatable condition and a body that falls under a court.
packet 附的來源說 amenable 來自 Anglo-Norman 的 amenable，再往前是 amener（帶來、引進），而 amener 是 a- 加 mener（帶領）。今天三個用法都還留著那個「牽」的畫面，所以同一個形容詞才能同時蓋住一個好商量的人、一個治得動的病，和一個受法院管轄的對象。
Wiktionary, "amenable"
登入就可以看每一支怎麼連回核心畫面。