PROBLEM: The printer itself can yes, HOWEVER, you can not auto duplex w/out buying an accessory.
BACKGROUND: I have included a page right from the HP6500 Series manual for you to view in which it notes that the printer does not support manual duplexing which means it would print on one side of the paper, when it comes out, it would wait for you to feed it back into the printer the other way. The printer supports automatic duplexing which means the printer prints on one side, and automatically re-feeds itself in and prints on the other side. In order to do this, you must purchase an HP Automatic Two-Sided Printing Accessory which I have included a link to here that would be clipped onto the front of your printer.
SOLUTION / WORK-AROUND: What can you do w/out having to buy the accessory? Well, you can fool the printer into manual duplexing. To do this, you would either put one piece of paper in the tray, let it print, then put it back in the tray upside down. Or, if you are doing a couple pages, say you are doing 10 pages, print your document, however when the box pops up to print, tell it to only print even pages, it will print those 5, then same thing, flip them over and put them back in the tray and print odd only.
Yes, a hassle, however unfortunately the 6500 series was not able to auto duplex w/out the add-on tray.
Thank you for using JustAnswer!