What do you think he wants?是个特殊疑问句。相应的陈述句是You think he wants something. 就这个陈述句划线部分提问时，首先用what替换something，再将what前置于句首，疑问词前置则导致部分倒装，于是得到What do you think he wants?

Do you know what he wants? 是个一般疑问句。相应的陈述句是You know what he wants. 陈述句改为一般疑问句只需将操作词倒装，原句没有操作词则加操作词do, does或did. 句末用问号即可。因此这个陈述句的一般疑问句为：Do you know what he wants.

网友之所以对这两个问句的形式产生疑惑，是因为忽略了一般疑问句和特殊疑问句的差异。