Is it possible to connect 2012 iMac as a second monitor to my 2024 MacBook Air?

Well, sort of. You can't use it directly since Target Display Mode, which is what dialabrain was almost certainly referring to, isn't supported on your Macs. You could use a third-party solution such as Luna Display, but that's suitable only for low-motion uses such as keeping tool pallettes on, and requires either a very good Wi-Fi network or Ethernet to work without lagging so much it would drive you crazy. You could give that a try, but if you want a second display for your MBA, you'll probably be happiest with an actual external display.

Regards.

+1 on the advice already offered.

Typically misquoted on other sites by "web gurus" having neither editorial assistance nor basic research skills, the very restrictive hardware and operating system requirements for the now-defunct Target Display Mode are laid out for all to see in this Apple support article:

Use your iMac as a display with target display mode - Apple Support

Apple administered the coup de grâce to TDM in early 2020. It dead tech.

As mentioned you could use Luna to do this however don't expect good performance. It is much more wise to buy an external display if you need one for your MBA. Why, simple:

• Doesn't require complex, expensive and slow software.
• No worrying about software licensing issues.
• Dead simple to set up.
• Dead reliable.
• Inexpensive, external displays are easy to find for <$100

Although 2012 iMacs support Target Display Mode, using Thunderbolt input, Apple added restrictions on Target Display Mode. Neither your 2024 MacBook Air, nor any other recent Mac, can use any iMac as a Target Display.

Nope.