Question

he offered to let him play with hem,(but)the boy said

为什么不能填then?有没有存在相似的情况的单词

Answer 1

说白了，这涉及到英语的基本结构，两个单独的英语句子不可以简单的用逗号连接，要么中间加并列连词变成并列句，要么把其中一个变成从句。如：
He was ill, he didn't go to school.是错的。可以改成：
He was ill, so/and he didn't go to school.
或者Because he was ill, he didn't go to school.

回到你的句子，but是并列连词可以用，then是副词不能用。

其实，还有一种办法解决要用到非谓语或独立主格，这要麻烦些，自己先看看再说。

Answer 2

如果是考试中的语法填空,,,有比较明显的转折建议首选but..
因为then差不多是万能的啊...还怎么考你...