The words are not synonyms. Take a look at the following: 1. I can hardly understand him = I can barely (only just) understand him. 2. I can roughly understand him = I can understand him to a certain extent, but noy very much. #1 is a negative statement. #2 is a positive stement.

Yes, there is a big difference between these two words: In this context, "roughly" means "approximately" e.g. "It's roughly five miles away." "Hardly" does indeed mean "almost none" so you can indeed say "I can hardly understand him." But be careful - it's an adverb so "I can hardly understand a conversation..." sounds a bit odd. You might want to find an adjective to describe the conversation instead: "His conversation was unintelligible to me."