Layover in MUC 6 hrs.

You need to get through passport control. The airport is about 45 minutes outside of Munich old town, so that will eat up about two hours, and you need to return to the airport at least two hours in advance of the next flight.
Hmmmm.....

I have been to Munich and flown out of Munich but never on a time crunch. I would be tempted to do it especially if you can get out of the MUC airport quickly. Even if you only had two hours to explore, you could do the RS walking tour and enjoy yourself much more than sitting inside the airport.

You need to get through passport control.

There is no passport control on an Amsterdam - Munich - Athens itinerary as the Netherlands, Germany and Greece are all in the Schengen area.

I'd still tend to agree that 6 hours is in the annoying space of "too short for an excursion, too long to be pleasant," but you won't have at least to go through passport control.

Kinda. Rome2rio suggests a 38 minute train ride. Assuming you've checked your luggage through to Athens (if any) you could catch the train (say 13-13:45), spend two hours, catch the return train at 15:45, then at 16:25 go through security, You'd be dragging your carryons with you unless you find a place to store them (which eats into your time). It won't be fun if you're jet lagged.

If you don't already have airline status affording you access to an airline lounge, I would consider buying a day pass or whatever is offered for your situation. I would not dare leave the airport for the time gap you have, certainly would not rely on the trains like that to go to Munich city center...

"There is no passport control on an Amsterdam - Munich - Athens itinerary as the Netherlands, Germany and Greece are all in the Schengen area.
I'd still tend to agree that 6 hours is in the annoying space of "too short for an excursion, too long to be pleasant," but you won't have at least to go through passport control."

We originally booked our direct flight from AMS to ATH with Transavia 3 months ago. Then 2 weeks ago, Transavia canceled the whole flight. We had to book a last minute flight with Lufthansa. It was a last minute idea with the layover to see if it is doable.

This is what I needed to know. Passport control going from AMS to MUC to ATH. With that said, what can I do for 2 hours in the city center?

Marienplatz is about a 15 minute walk from the Hauptbahnhof. With 2 hours, I’d probably wander around the pedestrian area there. There is a Rick Steves walk that covers that area if you want something more formal. You could also get lunch and a beer at the Hofbrauhaus or Augustiner Keller.

No need to stop at Hauptbahnhof and walk to Marienplatz since all airport suburban trains stop at Marienplatz as well.

But I would not go inside a beer hall when the weather is good. Walk to Viktualienmarkt (5 minutes walk from Marienplatz) and enjoy the beer garden there :-)

Thanks for everyone's insight. The last time we had a 7 hr. layover in FCO, we choose to stay at the airport. This time, I think we will try and visit the city center for a couple of hours.