iMac( 21.5-inch, Mid 2014) connecting with Mac Studio
Is it possible to connect Mac studios with an iMac (21.5- inch, Mid 2014)
Question marked as
In what way?
If you're asking about using the Mid-2014 iMac as a Target Display Mode display for the Mac Studio, you can't do that. The current requirements for "the other Mac" preclude that.
Use your iMac as a display with target display mode - Apple Support
Just to make a Thunderbolt data connection, you'd need $80 in hardware – a $50 TB3-to-TB2 adapter and a $30 TB 1/2 cable. Considering that that iMac has only a 21.5" 1920x1080 screen, and that monitor prices & specs have improved a lot in the last decade or two, you'd be better off putting the $80 towards a new standalone monitor.
If you're talking about transferring data between the two, you could use an external hard drive or USB flash drive to move data. I believe you could also connect the machines to each other using Gigabit Ethernet. That's the fastest speed the 2014 iMac's built-in Ethernet can support, and the slowest speed that the Mac Studio's built-in Ethernet can support.