Apply Kirchhoff law in loop I, −9+6I1+12(I1+I2)=0 18I1+12I2=9 6I1+4I2=3‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) Apply Kirchhoff law in loop II −6+15I2+12(I1+I2)=0 12I1+27I2=6 4I1+9I2=2‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) From equation (I) and (II), I1=0.5A I2=0