Find equivalent resistance between the points A and B.

Given figure is,

Here equivalent resistance in for parallel connection of $R$ and $2R$,

${\mathrm{R}}_{\text{total }}=\frac{{\mathrm{R}}_1\times {\mathrm{R}}_2}{{\mathrm{R}}_1+{\mathrm{R}}_2}=\frac{R\times 2R}{R+2R}=\frac{2}{3}R\left(\because {\mathrm{R}}_1\mathrm{\&}{\mathrm{R}}_2\text{ in parallel }\right)$

Similarly equivalent resistance in for parallel connection of $(2/3)R$ and $2R$,

$$\begin{gathered} {\mathrm{R}}_{\text{total }}=\frac{{\mathrm{R}}_2\times {\mathrm{R}}_3}{{\mathrm{R}}_2+{\mathrm{R}}_3}=\frac{(2/3)R\times 2R}{(2/3)R+2R} \left(\because {\mathrm{R}}_2\mathrm{\&}{\mathrm{R}}_3\text{ in parallel}\right) \\ {\mathrm{R}}_{\text{total }}=\frac{4/3}{8/3}R \\ =\frac{R}{2} \end{gathered}$$