conjunctions - Are there rules about using "that" to join two clauses?

He will understand that I was not joking.

He will understand I was not joking.

Which of the sentences is correct? Are there any specific rules about the use of "that" in the sentences I reported as an example?

Answer

That can almost always be dropped. In your example, that is being used as a conjunction, i.e. it is introducing a subordinate clause as the object of the main sentence. In most situations where this is the case, it can be dropped. I cannot think of any where it can't be dropped.

When that is used as a demonstrative pronoun, e.g. "that was a nice question," it must be kept or replaced with another pronoun, e.g. "yours was a nice question."

When used as a relative pronoun, it can usually be dropped. For instance, "several people read the question that you wrote" can also be "several people read the question you wrote". But if used in a question with who, it should be kept. For example, "Who was the person that wrote this question?" cannot be *"Who was the person wrote this question?".

I'm sure I missed something, but the comments should keep me honest.