The issue is that if you are using a 12V supply and you get a 24V LED it can only use half of it's rated lumens (if it even turns on, some LED's will not activate without a power supply that is within 3-4 volts). Bascially it will be dim as heck if it turns on at all.
Rule of thumb is you should always match your LED's Voltage to the Battery or transformer size. Everything should be the same Voltage (or have the same voltage range if you are using a transformer) There are nuances of course, but it gets a little detailed.
Hooking up a 3-6V LED will probalby burn out immediately when it is turned on or soon after. It is getting too much voltage for the diode to handle.