How much cake batter to make two 6"x2" cakes?

It depends upon how thick you want it. A 6"x2" rectangular pan, filled 1" deep will obviously contain 12 cubic inches of batter. 12 cubic inches = .83 US cup. So, to fill both pans to a depth of 1 inch, you would need 1.66 cups. To fill both pans to a thickness of 1.5 inches, you would need 2.49 cups. To fill both pans to a depth of 2 inches, you would need 3.32 cups of batter.

That's a 6X2 inch rectangle, of indeterminate depth, which is how I interpreted your question. A round pan with a diameter of 6 inches would hold 28.3 cubic inches of batter for each inch of depth. 28.3 cubic inches equals 1.98 cups.

Here's a conversion site for cubic inches to cups.

A 6"x2" rectangle is an odd shape and size, so I included an answer to another possible interpretation of your question. Please comment, especially if you don't feel that I've fully answered your question.