What is the current through the 6 Ω resistor?
Simplify the circuit.
3 Ω in parallel with 6 Ω = 2 Ω
2 Ω in series with 4 Ω = 6 Ω
i=\frac{6 V}{6 Ω}=1 A
R_{parallel} = 3 Ω
R_{total} = 3 Ω + 6 Ω =9 Ω
i=(1 A)\left\lgroup \frac{3 Ω}{3 Ω+6 Ω}\right\rgroup=1/3 A