Mac mini late 2014, how do I get maximum 2550 x 1660 resolution on external screen. What cables and ports do I use?

The HDMI port can't support resolutions greater than 1080p at 60Hz.

Mac mini (Late 2014) - Technical Specifications

"HDMI video output

Support for 1080p resolution at up to 60Hz

Support for 3840-by-2160 resolution at 30Hz

Support for 4096-by-2160 resolution at 24Hz"

What display do you have?

If its a Thunderbolt display, connect it to one of the Thunderbolt ports.

Any other type will use a Mini DisplayPort cable or adapter from one of the Thunderbolt ports. Do not use the Mac mini's HDMI port for 2560 X 1600.

@steveKJ: On the 2014 Mac mini, you would need to use either of the Thunderbolt 2/mini-DisplayPort ports to achieve this resolution.

@Malcolm J. Rayfield: Sorry Malcolm, I replied to your tread by mistake.

"why is it best NOT to use HDMI.."

Because the original incarnation of HDMI was for use with HDTVs (1920 x 1080 aka 1080i), not computer monitors. MiniDisplayPort was designed for use with computer monitors. Later versions of HDMI have higher resolution capability.

See: https://en.wikipedia.org/wiki/HDMI

Hi Steve, go to the Displays preferences, hold the Alt (option) key and then select the Scaled button.