Is HP Laser Jet 2420n

If your printer does not have a duplex unit then the printercannot print double sided pages automatically.
You can print double sided pages but you have to do it one page at a time.
For details, please click on this link and follow my instructions :- http://www.fixya.com/support/r7325259-double_sided_printing_using_single_sided

Do you have the 1320D or just a 1320. Only the D version will duplex automatically. The base version requires you to manually duplex. If you are sure you have the duplex version, then check the settings in the print driver and make sure it shows that the duplex option is installed. The driver often defaults to no duplexer.

HP P4515n is not a duplex printer by default. It is a network printer. ('n' suggests it is a network printer. Duplex printers have 'd' in the model number).
If you want to print both sides, manually feed sheet by sheet. Or else you can do the following:
If you are using, say MS Word, print only the odd pages (Print the normal way. No need to manually feed paper). Then arrange the printed papers in the proper order and keep the printed side as back side. Insert the set of papers in the printer and print only the even pages.
First print a document of about 6 pages to get the hang of it.

Click Start
Click Control Panel
Click Printers
Select the HP printer
Configure it to "double-sided" or "duplex" mode.

You have to print the first side then take those prints and put them back into the paper tray to print the second side (Manual Duplex). If this were a DN model it would have built in automatic duplexing and you cound select "duplex printing" from your print setup screen and the printer would print both sides automatically.

check your software, and printer settings

HP Laser Jet P3005s Network Printer doesn't print on both sides so you need to do that manually.

Yes it is.
HP LaserJet P3005n Printer (Q7814A)

Specs:
Duplex printing (printing on both sides of paper)
Yes: Automatic (standard)

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To prevent this you would have to set printer for single sided printing. This is an automatic feature in hp printers mine does the same thing.

I believe you are being referred to the "Users Manual"
Do you still have the book that came with it?