how to determine the current in this circuit
A simple approach to this problem is the following (I will leave the details of the calculations to you): Find the equivalent resistance of the 3 and 6 ohm resistors. Consider that resistance with the 4 ohm resistor as a voltage divider.  That will give you the voltage across the 6 ohms resistor. Ohm's law will then give you the current through the 6 ohm resistor.  If you do these calculations correctly, you will find that the current in the 6 ohm resistor is indeed 1/3 ampere.