Handbrake Cable adjustment

What kind of car do you have? If it's a Hyundai then there are no adjustment points for the cable. These cars have a self adjuster in the rear brakes. Only thing I can suggest is to remove the rear drums and manually adjust the shoes as needed. Adjust the shoes out until you feel a drag on the drum. Replace the drum and try the hand brake before replacing the tire, you save time this way in case more adjusting is needed.