I am connecting a double oven that has a 10 gauge 4 wire cable coming out of back to a 10 gauge 3 wire cable that runs to the main panel.
How should I accomplish this?
The National Electrical Code allows an existing 3 wire cable to feed a new oven.
Here is the pertinent article from the 2014 NEC:
250.140 Frames of Ranges and Clothes Dryers. Frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be connected to the equipment grounding conductor in the manner specified by 250.134 or 250.138.
Exception: For existing branch-circuit installations only where an equipment grounding conductor is not present in the outlet or junction box, the frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be permitted to be connected to the grounded circuit conductor if all the following conditions are met.
(1) The supply circuit is 1201240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.
(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.
(3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE service-entrance cable and the branch circuit originates at the service equipment.
(4) Grounding contacts receptacles furnished as part of the equipment are bonded to the equipment.
If all of 1-4 are true you can do it.
The oven should have a bond strap from the manufacturer to allow the bonding of the neutral and ground on the oven. And then you can connect both the ground and neutral from the oven to the neutral wire from the 3-wire cable.
Good luck and stay safe!