Unable to update software in my MacBook Air

 How to Upgrade to macOS 12 Monterey

❗️– WARNING – Backup your data before proceeding. (You’ve been warned.)

Learn How to Back up your Mac with Time Machine:

Back up your Mac with Time Machine - Apple Support

❗️ – IMPORTANT – If upgrading from 10.14 Mojave or earlier, your older 32-bit 

apps & drivers won’t work in Monterey! They must also be updated or replaced.

Use this free utility> Go64 app from St. Claire Software to check your apps

✅ - Click on Apple menu  > System Preferences… > Software Update.

If your Mac does not offer an OS upgrade in System Preferences…, download the macOS 12 Monterey installer from the App Store.

The download will place the "Install macOS Monterey" app in the Applications folder. Double-click that installer app to begin the upgrade process. 

Bayfischer wrote:

I want to update a Macbook Air, 2017 or 2018, 10.13.6, 8 Gb to Monterey

Your screenshot shows that you have a MacBook Air (13-inch, 2017). You can upgrade macOS as far as Monterey, but no further. (Be aware that Catalina, Big Sur, and Monterey do not support 32-bit applications.)

How to download and install macOS - Apple Support

I don't even get any response when choosing 'software update' from the 'about this...' menu. If that is solved how do I get Monterey without going to something newer?

That does not make sense. Going from High Sierra (10.13.*) to Monterey (12.*) is by definition going to something newer.

You may want to make a bootable clone backup of High Sierra onto an external drive before upgrading macOS – just in case something goes wrong, and you need something to use while you regroup and recover. If you kept an external drive with High Sierra around, that might also give you a way to dual-boot, so you could continue to play old 32-bit games every now and then.

If you're unable to update your Macbook Air through the "Software Update" option, you can directly download and install macOS Monterey from the App Store. Just search for "Monterey" and follow the on-screen instructions to upgrade your system hassle-free.

You're welcome.