${\mathrm{i}}_{1}+\mathrm{i}_{2}=\mathrm{i}_{3}$          ........$(i)$

Using Kirchoff's loop law in closed path abcda.

$10.0-(6.0) \mathrm{i}_{1}-(2.0) \mathrm{i}_{3}=0$

or $\quad(6.0) \mathrm{i}_{1}+(2.0) \mathrm{i}_{3}=10.0 $        ..........$(ii)$

Similarly for loop befcb we have $-$

$-14.0-10.0+(6.0) \mathrm{i}_{1}-(4.0) \mathrm{i}_{2}=0$

or $\quad(6.0) \mathrm{i}_{1}-(4.0) \mathrm{i}_{2}=24.0$

From Eqn. $(i)$ and $(ii)$ 

$\mathrm{i}_{1}=2.0 \mathrm{\,A}, \mathrm{i}_{2}=-3.0 \mathrm{\,A}$