Driving your Mazda 6 with a broken taillight increases your risk of both getting a "fix-it" ticket and being involved in a collision. Fortunately, replacing the bulb only takes a few minutes and is easy enough for someone without mechanical expertise to do.
Turn off the car's engine, activate the parking brake and take the keys out of the ignition before starting.
Open the trunk by using the driver's side trunk release latch or by manually unlocking it.
Locate the plastic trunk trim retainers. Pull out on their center knobs to remove them from the trim, and then peel back the trim to expose the taillight bulb sockets.
Twist the bulb socket quarter-turn counter-clockwise to remove it from the taillight assembly. Then, pull the broken bulb straight out of the socket and dispose of it immediately.
Insert the replacement bulb directly into the empty socket, and then twist the socket back into the taillight assembly.
Test the new light to make sure it's working. If everything checks out, replace the trunk lining, press the plastic fasteners into their holes and close the trunk.