I'm not a teacher, but "what", for example can be used as:
A pronoun, as in: "What did he do next?"
An adjective, as in: "What book are you reading?"
An adverb, as in: "What does it do?"
An interjection, as in: "What!"
"That" can also be used in many ways
It would help if you could provide similar examples of the context in which the difficulty arises.
You may also find the following URL of assistance - search for "what" & "that" for examples of their usage in context:
Online Dictionary, Encyclopedia and Thesaurus. Free access.