Just to clarify....when you say "double breaker", you need one like this that is two breakers with a common trip. This will use two spots in the panel and ensure that the circuits are out of phase so they can share a neutral. In this case you can use either 10/3 UF cable OR run 4 THHN conductors in 3/4" conduit, usually red and black for the hots, and a white for the neutral and green for the ground.
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IF you are referring to the unit on the left ion the pic below as a double breaker, you MUST run separate neutrals for the 2 circuits since they will be on the same phase, and you will overload a shared neutral. Not a big deal, just add another white in the conduit.
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