can I install monterey on a 2012 macbook air running Yosemite 10.10.5?

No possible . Does the >>  Computer Qualify for the Monterey upgrade 

The best this computer might do in macOS 10.15 Catalina

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

macOS Sierra 10.12 hardware requirements

OS X El Capitan - Technical Specifications

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Sorry, no. If you read the related article at the top of this page you see that the cutoff for Monterey for the MaBook Air is 2015.