Both your containers need share at least one network. It looks like have created a external network. Good job. The next step is to configure your container to join the network. Do something like this:

services:
  nginx-proxy-manager: 
     ....
     networks:
       - nginx-proxy-manager_default # or just nginx
      ...

networks:
  nginx:
    name: nginx-proxy-manager_default
    external: true  

Don’t forget to also add the network in your audiobookshelf service.

Maybe this helps: docs.docker.com/compose/how-tos/networking/#use-a…