If 6.5 hrs is time between one arrival and other plane departure, you'll be really limited but not impossible depending on time of day, how busy immigration/customs are.
If your luggage is being checked through, and you dash from aircraft to immigration and then on to customs with just a shoulder bag or whatever, make sure you have a chockie bar in it to declare as you will get through the red declarations line quicker than the green line where you can get held up just because of more people there and then some getting selected at random.
There are trains from the airport leaving about every twelve minutes, and takes about 20-25 minutes to get from airport to Circular Quay station, costs about $22 return.
If you are there within two hours say, down at the Quay where ferries leave from, either 15 minutes on a Jet Cat (dearer) or 30 minutes to see Sydney from the harbour slower,
Sydney Transport details and do it slow one way, faster the other and you have probably got time to either have a quick walk yo the ocean side or just enjoy a trip to Manly and back for a splendid way of seeing some of Sydneys best features and then use extra time for a walk about the Rocks area before getting a train back to airport, checking in without luggage, if you are there an hour before flight, you would be OK.
Alternately, forget doing the Harbour both ways and use the extra hour or so to enjoy your walk around the Rocks (adjacent to the Quay) and also to take in a walk around to the Opera house side, even on into Botanical Gardens a bit.
Edit Seeing as station names will be unfamiliar to you, its International Airport and Circular Quay,
timetable page here and Rocks Area if you do not know it is the historical heart of Sydney, where first settlement landing was.
But you're coming halfway around the globe, not to have more time in Oz?!