I find learning English difficult.（difficult是形容词做宾补）

解答：形容词作宾补正确

I saw the kite up and down.（up and down是副词做宾补）

解答：正确

We consider him a good teacher.（a good teacher是名词做宾补）

解答：正确

I found him in trouble.(in trouble是介词短语做宾补)

解答：正确

请问老师，是不是所有的名词形容词副词介词短语做宾语补足语的时候，都是省略了不定式to be呢？谢谢老师的回答。

解答如下：

不是所有动词，是有些动词，可以看作为省略不定式to be

We think Tom (to be)an honest boy.

We consider Tom (to be) very clever

动词后面可以用“ to be + 名词、形容词或介词短语”作宾语补足语。有这些动词 believe， declare， find， imagine， judge， prove， report， think 和 deny， discover， feel， guess， know， suppose， understand 等也都属于这类动词。

【1】这些动词的这一用法常用于正式文体。

　They all believe the story to be true.

　他们都相信这篇报道是真实的。

　He declared the story to be false.

　他断言这篇报道是假的。

　Imagine yourself to be in his place.

　设想你自己处于他的地位，那又会怎么样呢？

　We judged the distance to be about four miles.

　我们估计距离大约是 4 英里远。

　We all felt the plan to be unwise.

　我们都感到这个计划是不明智的。

　Fans know him to be a good player.

　球迷们都知道他是个好球员。

　Everyone reported him to be the best man for the job.

　人人都在传说他最适合做这项工作。

　I understood him to be a distant relation.

　　我猜想他是个远房亲戚。

【2】在被动句中， to be 短语应为句子主语的补足语。

　Money was also thought to be very important.

　钱也被认为是很重要的。

　The speaker's supposed to be excellent.

　这位演讲人被认为是很优秀的。

【3】作 believe， consider， declare， find， imagine， judge， prove， report 和 think 等及物动词的宾语补足语或主语补足语的 to be 可以省略。

　I found him （ to be ） much younger than I had expected.

　我发觉他比我原先预料的要年轻得多。

　I thought him （ to be ） too old for the work.

我认为他太老了，不适合做那项工作。

　Her work is considered （ to be ） the best here. 

　在工作方面她在这儿被认为是最好的一个。

　He was proved （ to be ） wrong.

　他被证实是错的。

　但 to be 是完成形式时，却不能省略。

　We believed it to have been a mistake.

　我们相信那曾是个错误。

【4】 在非正式文体中，这些及物动词后面的复合宾语可由 that 引导的宾语从句取代。

I guessed him to be a doctor by the way he spoke. 

= I guessed that he was a doctor by the way he spoke.

我从他讲话的方式猜想，他是个医生。

She denied herself to have been there. 

= She denied that she had been there.

她否认自己曾经去过那里。

The film is believed to be the best this year.

 = It is believed that the film is the best this year.

这部电影被认为是今年最好的。

The man was later discovered to have been a spy. 

= It was later discovered that the man had been a spy.

后来，发现这个人当过间谍。