Thevenin's equivalent
Yes your analysis to find the thevenin resistance is spot on. Regards the voltage and that confusing current source, what I'd do is split that current source so that it takes 3 amps from node a to node b and another current source of 3 amps injects 3 amps into the junction of the two 10 ohm resistors: -

 

I do it as a visual aid to help me see things clearer. Your original circuit with the voltage source converted to a 2.4 amp current source in parallel with its 10 ohm resistor is on the left. On the right is the split current source(s) and as you can see, my sim tells us that this idea produces exactly the same results but the circuit on the right is easier to work out.

For instance I can now parallel I3 and I4 like this: -



Then convert back to a voltage source of 54 volts in series with 10 ohms: -



Then convert the 54 volts to a current source of 2.7 amps in parallel with 20 ohms: -



And you can probably see that if I combine the 20 ohm and 5 ohm parallel resistors I get 4 ohms and this adds to the 16 ohms to give you a thevenin resistance of 20 ohms....

.... But I don't see how you can get a thevenin voltage of 11.2 volts so I think you have made a mistake somewhere. Clearly I haven't!