He suggested that she()improve her oral English by doing a lot of practice.wouldshouldmaymust

He suggested that she()improve her oral English by doing a lot of practice.wouldshouldmaymust
He suggested that she()improve her oral English by doing a lot of practice.
would
should
may
must

He suggested that she()improve her oral English by doing a lot of practice.wouldshouldmaymust
should,表示应当

would

should
这是虚拟语气中的一种简单用法,也可以省去

should
他建议她（该）通过大量练习来提高口语

should 这是虚拟语气,可省 因为suggeste这里是建议的意思
同时,这也是固定用法