Confused about circuit analysis example
Assuming the 12V voltage source is supposed to be an ideal voltage source it forces 12V across the 4m resistor. It doesn't matter what the 6V source and its resistors do. The voltage across the resistor is 12V and therefore the current through it is fixed by Ohm's law I=V/R.

Any eventual currents caused by the 6V source will be taken into account by I3.