Point A and B are at same potential so they can be merged/folded.

For loop 1

$$ \begin{aligned} & -\frac{1}{2} x-\frac{1}{2}(x+y)-x+6=0 \\\\ &\Rightarrow -2 x-\frac{y}{2}=-6 \\\\ &\Rightarrow -4 x-y=-12 \\\\ &\Rightarrow 4 x+y=12 .......(1) \end{aligned} $$

For loop 2

$$ \begin{aligned} & \frac{1}{2} y+1 y+12+\frac{1}{2}(x+y)=0 \\\\ &\Rightarrow \frac{3}{2} y+\frac{y}{2}+\frac{x}{2}=-12 \\\\ &\Rightarrow 2 y+\frac{x}{2}=-12 \\\\ & \begin{array}{l} \Rightarrow4 y+x=-24 \\\\ \Rightarrow4 y+x-16 x-4 y =-24-48 \end{array} \\\\ &\Rightarrow -15 x=-72 \end{aligned} $$

$$ \Rightarrow $$ $x=\frac{72}{15}$

$$ \Rightarrow $$ $4\left(\frac{72}{15}\right)+y=12$

$$ \begin{aligned} \Rightarrow y & =12-\frac{288}{15} \\\\ & =\frac{180-288}{15} \\\\ & =\frac{-108}{15}=-7.2 \mathrm{~A} \end{aligned} $$

Current in $R_1=7.2 \mathrm{~A}$

Current in $R_2=\frac{x+y}{2}=\left(\frac{72}{15}-\frac{108}{15}\right) \frac{1}{2}$

$$ \begin{aligned} & =\frac{1}{2}\left(\frac{36}{15}\right)=\frac{2.4}{2} \mathrm{~A} \\\\ & =1.2 \mathrm{~A} \end{aligned} $$

Current in $R_3=x=4.8 \mathrm{~A}$

Current in $R_5=\frac{1}{2} x=2.4 \mathrm{~A}$