What do I need in order to install under cabinet lights?
I just installed these under some cabinets, and they work great.

Most LED under cabinet lights are similar so...  Each "strip" is made to chain to the previous strip.  In my installation, the first strip is plugged into an outlet with the large transformer you have pictured, and then a 12v jumper goes from the first to the second, second to the third, etc.  I have 6 lights in a chain.

You installed 5x 120v drops...  You could have a transformer at location #1, #2, and #5, and chain #2>#3>#4 and #5>#6.  For each separate 120v connection you will need a duplex outlet and a 12v transformer.  For the lights that I linked, the barrel connector on the transformer needs an adapter to fit the smaller barrel of the lights, so pay attention to that as well.

Amazon sells the transformers and jumper wires separately, so you can buy them as needed.

Also note that your linked question is dealing with RGB "strip lights" that are cut-to-fit, so it's much more complicated than plain'ol white, modular LED lights.