Can I use an iMac 2014 as a display for a Mac mini
First of all, your 2014 iMac has to be a mid year model. The late models do not have target display mode.

You do realize you will need two keyboards for this to work. One for the Mac mini and one to put the iMac in target display mode. 

I assume the Mac mini is a 2018 year model. This model does not have any Thunderbolt 1 or 2 ports. There are USB-C ports where Thunderbolt 3 devices can be attached.

So, if this is going to work, you will need an adaptor. Apple sells a Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter for 49 USD. Next, you will need a thunderbolt 2 cable. Apple sells an Apple Thunderbolt Cable (0.5 m) - White for 29 USD. This is rather short, so you might want the Apple Thunderbolt Cable (2.0 m) - White for 39 USD.

So, 49 USD + 29 USD = 78 USD. You can buy a new 21.5" 1920 x 1080 monitor for 70 USD. Granted, this monitor does not come with a  HDMI cable, so you might need to buy one.


  The point is, you can buy a new monitor with the same size and resolution for about the same cost as the adaptor plus cable needed to use your old iMac as a display.


Note: the 2018 mac mini does have a internal speaker.