b
Applying junction law at $H$
$I_{H G}=i-\left(\frac{i}{2}+\frac{i}{6}\right)=\frac{i}{3}$
Applying junction law at $G$
$I_{H G}=\frac{i}{6}+I_{G B} \Rightarrow I_{G B}=\frac{i}{6}$
Applying junction law at $B$ .
$I_{B C}=I_{G B}+\frac{i}{6}=\frac{i}{3}$
Applying junction law at $C$
$I_{B C}+\frac{2 i}{3}+I_{F C}=i \Rightarrow I_{F C}=0$