Do I need a re-entry permit for a 6 month multiple entry visa in Thailand?

In case you need a re-entry permit (which means you want to travel during the last entry from your visa), you need to go to the local immigration office to apply for one. You can get one at the international airport just before departure. But most land borders don't sell re-entry permits to foreigners.

You don't need a re-entry permit with a multiple-entry visa. It's valid for multiple entries already.

If you will enter Thailand again BEFORE the "valid until"/"visa must be used by" date, you don't need a re-entry permit and you will be stamped for whole new 60 days. If you will enter Thailand AFTER those dates and you want to enter on the remaining days of your current stamp, you will need a re-entry stamp. Be aware, the re-entry stamp wouldn't add any days to your current stamp.

You might be able to get some idea about visas from the attached.