Can MacBook Air M2 connect to iMac late 2014?

If you are asking whether you can put the iMac into Target Display Mode to use it as a monitor for the M2 MacBook Air, the answer is No.

Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014. (That would be your iMac, since the 27" 5K model was the only one that came out in Late 2014.). Apple later added restrictions that mean that your M2 MacBook Air is too new to support using any iMac (even an older one) as a Target Display.

That iMac is too old to act as an AirPlay Receiver for AirPlay to Mac – a lower-quality way of using a Mac's display as a display for an iPhone, an iPad, or another Mac.

dollyp52 wrote:

Unfortunately I can no longer run MS Office for Mac on the iMac, so I was trying to see if I could use it as an extended display screen for my MacBook Air - but that doesn't seem to be the case.

There is a workaround product, called Luna Display, that might let you use that 27" Late 2014 iMac as an extra display for the M2 MacBook Air.

There are some significant practical obstacles to using it.

• You need to plug the Luna Display device directly into a USB-C port that supports DisplayPort. Plugging the device into a downstream port on a hub or dock is not supported.
• You would need to run a cable between the MacBook Air and the iMac to help carry video traffic.
• Even then, the connection would not be as good as with a hardware monitor, especially if you were trying to display rapidly-changing content (such as that associated with video editing or gaming).
• Your M2 MacBook Air only has two USB-C / Thunderbolt ports. So attaching your iMac via the Luna Display device and a cable would use up both of them, leaving no place to plug in other devices (like backup drives) unless you had a dock or a hub.
• If you had a dock or a hub, you could try connecting the cable to the iMac (not the Luna Display device) to it. But since that cable would be carrying a lot of video traffic, there might not be much bandwidth left over for other uses.

It may be easier to get a real hardware monitor for the M2 MacBook Air – or to get an alternative office program (such as LibreOffice) that will run on the Late 2014 iMac.

The current version of LibreOffice still supports Big Sur and later. (You would want the Intel download for your iMac, and the Apple Silicon download for your M2 MacBook Air.). The Document Foundation even maintains an archive of older, unsupported, versions of LibreOffice that run on systems as ancient as PowerPC-based Macs running Mac OS X 10.4.* (Tiger).)

connect for what purpose?

for filesharing? sure

Set up file sharing on Mac – Apple Support (UK)

remote desktop? sure

Apple Remote Desktop User Guide for Mac – Apple Support (UK)

there are ways though their performance would maybe be found wanting

try reading

Use iMac as monitor: 5 Solutions - 9to5Mac

and if the main issue is that your imac is no longer supported by microsoft then you can use libreoffice it's free and read and write ms office files

Free and private office suite, no forced AI — LibreOffice

also an imac use a lot! more electricity than a normal monitor so it would be more sustainable to not use the imac as just a display