Here are three another English books for you

three another English books 应为 three other English books

another 是泛指；other 特指除之前以外的其他。

问题就是应该改为“another three ”

因为表示另外的三本有两种方法
1 数词+more
2 another + 数词

其实就是位置的问题
比如：再给我2个苹果

give me another two apples

give me two more apples

以前高中的时候老师教了的

three another English books 改成
another three English books

改成here are the other three English books for you

it should be: Here are three other Enlglish books for you.