他"不"可能"不"知道答案 that means he must know the answer (it's impossible that he didn't know the answer) 他"没"说他"不"相信That means he may believe it. (literally means he didn't say he doesn't believe it)

It's same with double negatives in English, for emphasis. Every one likes her. => No one doesn't like her. "沒有"人"不"喜歡她。 Everything is possible. => There is nothing impossible. "沒有""不"可能的事。 He knew that. = > There is no way that he didn't know that. 他"不"可能"不"知道。

In case of "a double negative and then make the statement positive": Think about it in mathematics way. 不。。。。不。。。= 1不 - 1不=0不. As result, just focus on the end of sentence to get the truth meaning. Eg. 不能不说 which means, have to say. 不能不说她非常优秀=She is very excellent! .Eg.不偏不倚(刚刚好)=Just right! Eg没说不行 = Yes For your question, can be finished here. ( However, there are more meanings of double negative comes to one sentence. 1. Eg. 不说不行=must to say 2. Eg. 不想说不想听! Don't care at all! 3.Eg. 这支笔（既）不是你的，（也）不是我的，（而）是她的。This pen neither belong to you not me, but belongs to her.--- Well, in this case, 不。。。不。。。still equal to 1不 - 1不=0不, but does not make the statement positive. Therefore, it is same idea to understand one or two words from whole sentence or article in English. )

No such sentence structure in Chinese.It just like somebody said “no” twice, nothing more.

can you give an example?