hi...how can i use my hp deskjet ink advantage 2010 printer by using my Macbook Air (latest)? i cannot add a driver for it...

Hi,

Many printers that could be used on earlier operating systems do not have supported drivers for macOS 12 Monterey. Is this the operating system used by your Mac?

This does not necessarily mean that a driver installation is absolutely impossible, but anything you do will be entirely experimental. If you decide to proceed, make sure that you have backup copies of all important files (documents, photos, et cetera).

Does any driver software appear at all if you try to add the printer? Have you tried to reset the printing system?

Reset the printing system on your Mac to solve a problem – Apple Support (UK)

Add a printer to your printer list so you can use it on Mac – Apple Support (UK)

An HP Deskjet Ink Adv 2010 K010 series 2.3.2 driver is listed in the no longer updated article Printer and scanner drivers for Mac - Apple Support. Unfortunately, it says Not compatible with macOS v12 and newer for the Apple download at https://support.apple.com/kb/DL1888?viewlocale=en_US&locale=en_US (but we have seen one report about another printer driver from this download used with macOS Monterey). The driver version in the list can sometimes be a clue when looking for other (HP) printer models with compatible drivers.

There is an HP Easy Admin tool for Mac that allows administrators to download drivers without a connected printer. It may or may not be possible to find drivers here. If you find a driver, it may or may not be possible to install it.

https://support.hp.com/us-en/document/c06164609

AirPrint-enabled printers (About AirPrint - Apple Support) are compatible with macOS, and can be used without additional drivers. Unfortunately, your printer does not appear to be listed here, so other ways would have to be tested.