If you are new to running Plex on Synology, suggest you read the following documents:
- Installation & Setup of Plex Media Server on Synology
- Synology FAQ - Questions, Answers, and a few How-To’s
To directly answer your question, Plex is designed to work with private IPv4 addresses as defined by RFC-1918.
- 192.168.x.x
- 172.16.x.x to 172.31.x.x
- 10.x.x.x
Plex can work with valid public IP addresses (such as installation in a data center), but you have to jump through some extra hoops during initial setup.
