The potential difference between the point A and B is

I think the answer would be 3V, Let us assume voltage at A =0V, now convert the 2V , 1ohm and 4V and 1ohm resistor into current form by source transformation method. ex- 2v , 1 ohm can be converted as 2amp current source connected in parallel with 1ohm resistor. and similarly 4amp current source will be connected in parallel with 1 ohm resistor. 

So no current will go outside the loop. and the potential difference between A and B will be equal to 3v.