1.you should be more careful _your study(of /for)选什么为什么2.i saw bill___the room quietly and sit behind the door(enter/entering/come/enter into)

(1）for (2)enter into

1. You should be more careful for your study.
2.I saw Bill enter the room quietly and sit behind the door.（see +名词+不带to的动词不等式，表示看见...的整个过程）
【后接介词 of 或 about】表示“当心”、“留意”等。如：
Be careful of the dog; it sometimes bites people. 当心那条狗，它有时候咬人。
You must be careful of [about] your pronunciation. 你要注意你的发音。
【注：be careful 后一般不接介词 for】如：
我希望你要多注意身体。
正：I hope you’ll be more careful of[about] your health.
误：I hope you’ll be more careful for your health.
【后接介词 with(其后多接名词)或 in(其后多接动名词)，表示做某事时很小心或仔细】如：
He’s careful with [＝in doing] his work. 他工作很仔细。
Be careful with the vase; it is valuable. 这花瓶很贵，小心点。
Be careful in dealing with such people. 和这种人打交道要小心。

1、of
be careful of 小心,注意；当心…,对…仔细
2、enter
后面有信息词【and sit】
see sb do sth强调【动作全过程】.enter是及物动词,后面可以直接接宾语.