Did I solve the Thevenin equivalent circuit left of the terminals correctly?
You are correct.  The 2v source effectively eliminates the 6V source and the 6 ohm resistor in series with it since it is in parallel with those elements. Thus you are left with the 2V source across a simple voltage divider consisting of the 6 ohm resistor and the 4 ohm resistor. The voltage across terminals a and b will then be (4/(4+6)*2V or 0.8V. You are correct in that 1.2V is across the 6 ohm resistor.