multiple monitors - Connecting 2 laptops with docking stations to a split screen set-up

I work for 2 companies that require use of a docking station. I need dual monitor set-up for both docking stations. Is there a way to share a dual monitor set-up between the 2 docking stations? 1 is for a Dell and the other is HP. I am not sure what I would use to connect. A picture of the connecting part would be helpful as I am really only familiar with USB and HDMI ports.

Thank you in advance!