The problem with most students lies in the fact that they are too shy to speak English in public.

问题描述:

The problem with most students lies in the fact that they are too shy to speak English in public.
that they are too shy to speak English in public 是同位语从句吧?

是的.其先行词就是fact.同位语从句的先行词通常都是表示抽象含义的名词,比如说fact,problem,proof等.