We'd like to know the reason why you argued.

我们想了解一下你们为什么争吵？

Do I want to know the reason why lets me a thus hard choice?

我想知道什么原因让我如此难以抉择？

B.He wants to know the reason why(for which)he failed in the game.

他想知道为什么他会在比赛中失败的原因。（why引导定语从句修饰the reason）

In I'm tired of a day, the teacher want to know the reason why I disgusted, so please communicate parents go to school, I was there.

在我厌学的一段日子中，老师想了解我厌学的原因，于是请父母去学校交流，当时我也在。