Finding Norton voltage and resistance and max power
Your Vth and Rth value are incorrect.

One way to find Vth is to remove the load from your circuit. Vth will be the voltage between where the load used to be. In your case you need to remove RL and find the voltage between A and B.



The voltage between A and B is Vth.

Vth = I1 * R1 = 6A * 0.5 Ohm = 3V

Now to find Rth you can place a wire between where the load used to be and find the current flowing through that wire. Rth will be Vth divided by the current flowing through the wire. In your case you need to place a wire between A and B and find the current flowing through that wire.



The current flowing through R3 is Iwire.

Iwire = (R1 / (R1 + R3)) * I1 = (0.5 Ohm / (0.5 Ohm + 1 Ohm)) * 6A = 2A

Vth divided by Iwire is Rth.

Rth = Vth / Iwire = 3V / 2A = 1.5 Ohm

The correct value for Vth and Rth are:

Vth = 3V

Rth = 1.5 Ohm

Your P and Pmax formula are correct.