Please read these two documents. They will save you much time and trouble. There are several places where a Plex installation can go wrong. The documents will help you avoid them.
Installation & Setup of Plex Media Server on Synology
Synology FAQ - Questions, Answers, and a few How-To’s
Be aware that the version in the Package Center is outdated. Suggest you download directly from Plex and install the software manually.
The Installation & Setup document has details on performing a manual installation.
You should also be aware there is a problem with Intel’s linux driver for J4XXX CPUs. Because of the buggy driver, the system will not transcode video properly. You should configure your system to use the older driver. After installing Plex, see FAQ #26 for details on bypassing the buggy driver.