If you take the plinth off the front of the cabinet you should see four plastic feet, these are adjustable so make sure they are all touching the floor before you start. It is normally possible to cut the bottom off the side panels with a fine toothed hand saw (it depends what sort of access you have) but it is so much easier with a multi tool/multi-cutter. Since Fein's patent lapsed everyone makes one and the Dewalt one for about £100 works well. They are very noisy though so you will need ear plugs.

Either by hand or multi tool lay a scrap piece of flooring on the floor next to the side panel. Rest the blade on the scrap so that it supports the blade as you cut the side panel and you should get a perfect cut at just the right height.