1988 Cadillac Seville Mis-firing engine

About a year ago I had my car repaired because it was backfiring, and blew the muffler out. That problem has returned today. I looked at the bill for that repair and there is nothing said about what was done to fix the car, only that a muffler was installed, and that it back fired. Previous to the muffler blowout
the car was missing then as you drove it, it was fine. If I stopped for awhile and then restarted it would begin to miss again.
Any clue to what it might be?

Thank you for any help,
Robert