Does 6 gauge wire need to be in a conduit if run in a finished garage along the wall and ceiling?

If you are talking about #6 building wire, it needs to have mechanical protection. This means that it has to be run in conduit. If you are talking about #6 cable set like Romex, then it only has to have mechanically protection below a five foot elevation from the garage's finished floor. If the wall that the cable set is running in is going to be finished with drywall or plywood then that is considered protected.