How do I display my macbook pro screen on my IMAC monitor

If the lists of hardware and macOS requirements in that article are not clear, please post back telling us the sub-models and macOS versions installed on your iMac and Macbook Pro. Those are critical to what you can and cannot do with Target Display Mode (TDM). Conditions for using TDM are very limited, and Apple dropped hardware support for it in iMacs starting in Late 2014, and from all other Macs in Early 2020.

You can use network screen sharing but it will laggy: Share the screen of another Mac - Apple Support

If both computers are on Monterey, you can use Airplay to Mac, but demo videos on YouTube show it is also laggy. See the first topic on this support page:

System requirements for Continuity on Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support

Hi,

If you mean iMac screen as second display for your MacBook Pro, following document could help your question.

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

I use Network Screen Sharing to administer my Home Server in the basement.

I do not find it laggy, because the sharing is over Gigabit or 10 Gigabit Ethernet to my Router from both Macs.

I think doing the sharing over Wi-Fi (often at only 1/10 the speed) is what makes users report it is as laggy.

BUT: you can not expect full motion Video over Screen Sharing -- that is impossible.