have a rough time (of it)
To have a challenging period during which one struggles to do or cope with something. John had a rough time of it after losing both his job and his wife during the same year. I had a rough time repairing the engine because it was so rusty, but I eventually got it running again.
have a rough time (of it)
and have a tough time (of it)to experience a difficult period. Since his wife died, Mr. Brown has been having a rough time of it. Be nice to Bob. He's been having a rough time at work.