ok I'ts correct. So then i find or images Is synced at PM?+
I'm not sure I understand what you're asking.
Catalogs only know about what images you've added to them either manually (Include Selected Items) or via Scan to Catalog, Catalog Sync, or by adding them during Ingest. If those images are added and exist on your internal hard drive at the time then that is what is in your catalog. Having duplicates on your NAS will not be known to the catalog unless you also add the images on the NAS to the catalog (but then you'll have duplicates.)
I don't know if this helps you in your situation because you have not provided further details.
-Kirk