I wonder that what he wants to do

错, 去掉that .wonder 后面跟wh_ 词,表示不知道什么什么,。如-
I wonder why he was late again.
I wonder when to start .

不对 that去掉

不行，只能是i wonder what he wants to do

错，应该是：

I wonder what he wants to do.

宾语从句，应该是 I wonder what he wants to do ，他做的事让我很担心。