Touching the timestamp with "copy /b file.txt+,," and "type nul >> file" don't change the archive attribute here.
Former doesn't work here either. Latter doesn't work either. I think I may have mistyped >> as > at the command line (which definitely changes the file) when testing, because several of the test copies are empty.
I honestly think this is possibly the dumbest CMD-based question that could ever appear in a learning environment, because regardless of the "right way" to do it, it's trivia. I mean, when are you going to be without attrib, move, or other file management commands? At the very least you will ALWAYS have copy, so it makes the question moot.
I'd be with you on the Move command, but again, this is one of those dumb questions where the instructor arbitrarily limits your command set for no reason, and it seems like they have some specific solution in mind. Move as an answer could either be the desired answer, or be yet another arbitrarily unavailable command.
If nothing else, the OP ought to have learned to at least test provided solutions, rather than assume they work.