- I’ll be more careful what I say in the future.
- We were very careful that he didn’t find out.
The that-clause in sentence 2 is a complement of the adjective careful. The wh-clause in sentence 1 seems to be a noun phrase, rather than an embedded question, which I’m not sure of. Either way, I think the wh-clause serves a similar purpose as the th-clause does.
My question is, why is there no preposition governing the wh-clause?