All doors lock automatically when the lock side is pressed. They unlock when the unlock side is pressed.
Driver's door

Front passenger's door

To lock all the doors from an open front door, press the lock side of the door lock switch and then close the door.
NOTE
When locking the doors this way, be careful not to leave the key inside the vehicle.
Locking, Unlocking with Transmitter
Auto Lock/Unlock FunctionMazda 6 Owners Manual: Rocking the Vehicle
WARNING
Do not spin the wheels at more than 56 km/h (35 mph), and do not allow
anyone to stand behind a wheel when pushing the vehicle: When the vehicle
is stuck, spinning the wheels at high speed is dangerous. The spinning tire could
overheat and explode. This could cause serious injuries.
...
Mazda 6 Owners Manual: Fuel-filler lid and opener removal/installation
1. To remove the fuel-filler lid opener, remove the left side trunk side trim
(4SD) or trunk side lower trim (5HB).
2. To remove the fuel-filler lid opener cable, perform the following and turn
over the floor covering.
(1) Remove the driver-side front seat.
(2) Remove the driver-side fron ...