Question about “move up” VS “move down”, and “push” VS “pull”?
If we move up a meeting, it means to start a meeting earlier than it is supposed to. My question is if “move back a meeting” can mean “start it later”. Same question for “push” and “pull, “push an hour” means delay an hour, does “pull an hour” mean starting it one hour earlier?

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Yes, "move back a meeting' means that it will start later. "Pushing a meeting" also means to delay it. For example, "Let's push the meeting back one hour." The opposite is true for pull, someone can say, "let's pull the meeting forward one hour."