Sorry that sync on your Lightroom mobile and Classic is not working.
Which version of Lightroom Classic and Lightroom mobile are you using? Would you mind checking the steps below?
1. The Lightroom Classic CC app is not logged into the same Adobe ID as the Lightroom CC Ecosystem. (Help>Sign Out(AdobeID) 2. The currently open Lightroom Classic CC catalog is not the catalog, you've specified for syncing. (Only one catalog can sync with your Adobe ID at a time) 3. Syncing is paused in the Lightroom Classic CC App
Click on your Identity Plate to verify you are logged in and that syncing is not paused. If you see the word "Start" on the Syncing area it means you've designated a different catalog for syncing.