Your question concerns me as you may be heading for a fire. You need to run a new wire from the main panel to the appliance that is the safest way. Why? Well the 3 wire 220 doesn't have a common(white wire) and your appliance needs that. What that 4-wire cable does is provide two 110 volts and one 220 volts plus a ground to the appliance. The 3 wire 220 only provides one 220 volt and a ground. There is a way to cheat this but that is reserved for someone not asking the question you just asked :P as I wouldn't feel right if you messed up and either caused a fire or electricuted someone. Also make sure to use the proper wire gauge for your appliance, I'm saying this because of your question. If you're trying to connect a range to a wire that was use for a base heater(usually a 12 gauge black and white plus nacked ground inbeded inside a red insulator), don't do it, you're in for some fire trouble as most ranges will need an 3/8 gauge wire + ground ofcourse. If what I tell you doesn't help then let me know what power is required to run your appliance and what gauge, material and length is your wire(copper or alluminum).
