In steady state there is no current in capacitor branch, so equivalent circuit is shown in fig.

Net resistance of circuit,

Net emf, E = 6 V
Current in circuit, \(I=\frac{E}{R_{eq}}=\frac{6}{4}=1.5A\)
Potential difference across parallel combination of 2 Ω and 3 Ω resistance.
V = IR = 1.5 x 1.2 = 1.8 V
Current in 2 Ω resistance
\(I_1=\frac{V'}{R_1}=\frac{1.8}{2}=0.9A\)