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 \\
& -2 x-\frac{y}{2}=-6 \\
& -4 x-y=-12 \\
& 4 x+y=12
\end{aligned}
$
For loop 2
$
\frac{1}{2} y+1 y+12+\frac{1}{2}(x+y)=0
$
$
\begin{aligned}
& \frac{3}{2} y+\frac{y}{2}+\frac{x}{2}=-12 \\
& 2 y+\frac{x}{2}=-12 \\
& 4 y+x=-24 \\
& 4 y+x-16 x-4 y \\
& =-24-48 \\
& -15 x=-72 \\
& x=\frac{72}{15} \\
& 4\left(\frac{72}{15}\right)+y=12 \\
& y=12-\frac{288}{15} \\
& =\frac{180-288}{15}=\frac{-108}{15}=-7.2 \mathrm{~A}
\end{aligned}
$
Current in $\mathrm{R}_1=7.2 \mathrm{~A}$
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 $\mathrm{R}_3=\mathrm{x}=4.8 \mathrm{~A}$
Current in $\mathrm{R}_5=\frac{1}{2} \mathrm{x}=2.4 \mathrm{~A}$
