Find current in $6\,\Omega $ resistance
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$\mathrm{R}_{\mathrm{eq}}=[(2+1) \| 6]+3=5 \,\Omega$

$I=\frac{10}{5}=2 \,A$

$I_{1}=\frac{3}{9} \times 2=\frac{2}{3} \,A$

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