welcome to just answer
I researched the internet and unfortunately Hp didn't release a driver for this specific printer for osx 10.8
The latest driver available is for osx 10.7
did you try installing 10.7 driver
I am not done yet providing an answer so you can be able to rate the question
and the printer didn't come up under the print & Fax list ?
The HP driver update for OS X 10.8 (Mountain Lion) and most HP printers is available now from Apple Software Update (ASU)
Unfortunately your printer is among the printers that are not yet supported even through the ASU, so we are left with the following option which is to use Apple's Airprint to print on a network until the driver becomes available:
First of all you need to download and install the latest firmware update from hp website here: http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?os=4142&lc=en&cc=us&dlc=en&sw_lang=&product=4110410#N198
expand the + sign next to firmware and click the download button to be able to download it
when you are done you need to follow these steps in order to install the printer:
1- you must be connected to the printer through network connection
(not USB as the driver for the printer model is not yet available)
2- Turn on the printer and make sure that it is in a ready state.
3- Make sure that the computer has an active internet connection and that the printer is wirelessly connected to the wireless or wired (Ethernet) network (the same network subnet as your iOS device)
4- Make sure that Web Services is enabled on your HP printer.
5- Make sure that the HP product has the latest firmware version installed.
6- Click the Apple menu ([IMAGE][SRC][/SRC][ALT][/ALT][WIDTH]100[/WIDTH][HEIGHT]100[/HEIGHT][STYLE]border: 0;[/STYLE][/IMAGE] ), and then click System Preferences
6- Click the Apple menu and then click System Preferences
7- Click Print & Scan
8- Click the plus sign at the bottom of the left pane.
9- Under Nearby Printers , click the name of your printer.
10- Click the Use box, select AirPrint (if it is not selected already), and then click Add to add the printer to the queue.
Please follow these steps carefully and let me know how it goes. Don't forget to leave me a positive rating if you are satisfied with my help. A bonus will be highly appreciated.
If you have any further questions, i will be more than happy to answer them.
Next you need to follow those steps carefully in order to be able to use your printer with OS 10.8:
1-Turn on the printer and make sure that it is in a ready state.
3- Make sure that Web Services is enabled on your HP printer.
5- Click the Apple menu , and then click System Preferences .
6- Click Print & Scan
7- Click the plus sign at the bottom of the left pane.