Will my 2023 MacBook Air work with an LG 27UD68 monitor? Thank you!!

https://www.lg.com/global/business/monitors/lg-27UD68-W

I'm guessing that this is the monitor you have, or a closely-related one. (Sometimes monitor manufacturers add a "-W" to the end of the model name to indicate a white case, and a "-B" to the end of the name to indicate a black one. This doesn't affect how you connect to the monitor, only what it looks like.)

The specifications indicate that it is a a 27" monitor with UHD 4K (3840x2160 pixel) resolution. It has two HDMI inputs and one DIsplayPort input. So you could go with

• A USB-C (DisplayPort) to DisplayPort adapter or adapter cable, or
• A USB-C (DisplayPort) to HDMI adapter or adapter cable

You can find lots of adapters (which bring out a DisplayPort or HDMI socket) and adapter cables (which bring out a DisplayPort or HDMI plug, eliminating the need for a separate cable) on Amazon. Check that any adapter or cable supports 4K @ 60 Hz.

https://www.lg.com/us/support/product/lg-27UD68-W.AUS

There's an owner's manual on this site.

That question should be directed to the monitor's manufacture since they know what is or is not compatible.

FWIW, according to the LG set this monitor has been discontinued. Question is whether you can get support from LG on discontinued products.