my right rear door does not lock when i press the remote

The lock actuator may have died. The lock mechanism has rods that extend to the inside and outside door handles, and a rod that extends to the lock actuator. The actuator is what locks/unlocks the door by remote or from the driver door buttons. You'll have to remove the door panel to gain access to the actuator. They cost around 35-40. They're pretty straightforward to replace, although getting your hand inside the door can be a tight squeeze. Google how to replace a lock actuator for your make/model, there are usually plenty of youtube vids of that type of job. Couple tools you can pick up to make the job easier are: trim removal tools (get a cheap set from a store like Harbor Freight) and wobblers for a socket set. (they let you get around bends easier).