the reason that the reason why 的区别 the reason that he was la

首先,the reason that he was late was unknown 是错的,改正后应该是：The reason WHY he was late is unknown.=== The reason FOR WHICH(由于这个原因) he was late is unknown.
1 the reason why
把 Tell me the reason.和You were late for that reason合并起来,你就得到了the reason for,
----------- Tell me the reason WHY (==FOR WHICH) you were late.
翻译：告诉我他为什么不来/ 他不来的理由.
2 the reason that / which
把Tell me the reason.和He has given the reason for not coming合并起来,你就得到了一个定语从句；
------------- Tell me the reason THAT / WHICH (==THE REASON做GIVEN的宾语) he has given for not coming.
翻译：告诉我他所提出的不来的理由.

区别不大，你的表达是正确的

the reason that后面接的是reason的同位语，是reason的内容，可以与reason这个词互换的内容。而the reason why后面接的是why引导的定语从句，也就修饰reason的。
不对，应该是why，因为这里是修饰reason，你要表达的是“他迟到的理由”

不对，that改为why.这里使原因状语从句…

the reason that后面接的是reason的同位语，是reason的内容，可以与reason这个词互换的内容。而the reason why后面接的是why引导的定语从句，也就修饰reason的。
不对，应该是why，因为这里是修饰reason，你要表达的是“他迟到的理由”
这里使原因状语从句…...

不对。the reason why he was late was unknown.或者说he was late with the reason that ……x0cthe reason that……后面要接明确的理由。we can't go with the reason that x0cwe can't afford it。