Hello.
You can drill plexiglass no problem. You will need a good 3/16" drill bit. measure your plexiglass where you want the holes to be, then drill the plexiglass. Then hold the plexiglass up to your cabinet and predrill your cabinet with a 3/32" or 1/8" bit. If your cabinet has 3/4" sides, which are standard, if you dont predrill it, the wood is likely to split. You probably want to use a finish washer so the screw doesnt try to pull through the plexiglass.

If you need any additional tips or info you can email me.

Thanks
jason
ripken8@bellsouth.net