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When can you exclude "that" from a sentence?
There are a number of instances in English where it is possible and even desirable to omit that.
that as conjunction with reporting verbs (like learn, discover, find out, know, feel, etc.): I discovered (that) Julian had borrowed my car without my permission.
after the more common reporting verbs, (e.g. say, tell) it is also entirely natural to omit that in informal speech: I told him (that) I'd be back by ten o'clock but he said he needed me here by nine.
after certain verbs (e.g. reply, shout) that cannot be omitted and it is not normally dropped after nouns: The Dean of the Humanities Faculty informed the students that the drama dept was going to close.
Often, that can be removed from a sentence without affecting the overall meaning, especially when it has been used with a conditional, e.g. She told me that I could go to the party vs. She told me I could go to the party.
Sometimes, however, you can change or lose the meaning by removing that. For example, I heard that you snore = Person A snores, and Person B has told Person C about it, whereas I heard you snore = Person A snores and Person B has heard them doing it.
Consider whether your use of "that" is necessary for understanding time, object or person. If not, you can probably cut it.