We have no basement or attic access. Prior to remodeling my kitchen I ran a 6/3 wire (among others) to the kitchen before I drywalled the other room where the main breaker box is. Now I need a 12/3 for our electric cook top so I will need to add a sub panel and feed the 12/3 from the 6/3 with a double pole 20 amp breaker. My question is does this sub panel need to be exposed in the kitchen? Can I put it between the studs and make a cabinet cutout so it is accessible through the cabinet? I don't want a metal box mounted on the wall of my remodeled kitchen. Can I cover it with something like a hinged picture? Any other possibilities for covering this up? Thanks much for your anticipated help!

Whoa!

You need to back up, quite a bit. There is quite a bit more information needed before any one can assist you.

For instance, are you in the U.S.A. What is the Amperage required for the cook top (should be on the metal plate on the cook top). If you are in the U.S. I suspect that you need 30 amps for a range top. That calls for an independent 30 Amp circuit. You could direct connect your #6/3 to the range top, but you would only be able to use a 30 amp breaker.

What did you put in a #6/3 conductors for. #6 AWG (copper) is rated for 60 Amps!

The location of your subpanel can be in the immediate vicinity of your main panel.

#12/3 AWG (copper) is only rated for 20 Amps. If you connect those wires to your #6/3 wires, you will need to use a 20 amp breaker for the entire circuit.