Let $4\mathit{\Omega },4\mathit{\Omega }$ and $4\mathit{\Omega }$ are in series.


Now $2\mathit{\Omega },2\mathit{\Omega }$ and $2\mathit{\Omega }$ are in series.

${\mathrm{R}}_2=2+2+2=6\mathit{\Omega }$

Now ${\mathrm{R}}_1=12\mathit{\Omega },{\mathrm{R}}_2=6\mathit{\Omega }$ and $4\mathit{\Omega }$ are in parallel.
$\frac{1}{{\mathrm{R}}_3}=\frac{1}{12}+\frac{1}{4}+\frac{1}{6}$
$=\frac{1+3+2}{12}=\frac{6}{12}=\frac{1}{2}$
${\mathrm{R}}_3=2\mathit{\Omega }$
Now resistance between $\mathrm{A}$ and $\mathrm{B},5\mathit{\Omega },2\mathit{\Omega }$ and $6\mathit{\Omega }$ are in series.

Resistance between A and B, $\mathit{R}=5+2+6$ $=13\mathit{\Omega }$
Hence, Equivalent resistance between $\mathrm{A}$ and $\mathrm{B}=13\mathit{\Omega }$