The effective resistance between points A and C for the network shown in figure is:

$\frac{2}{3}$R

As R_AB = R_AO and R_BC = R_OC, so points O and B will be at same potential and hence, resistance R_OB becomes ineffective. Similarly, R_AO = R_AD and R_OC = R_DC, resistance R_OD becomes ineffective. So, excluding R_BO and R_OD, equivalent resistance R_eq of the given network between points A and C will be given by

$\frac{1}{R_{eq}}=\frac{1}{2 R}+\frac{1}{2 R}+\frac{1}{2 R}$ i.e., $R_{e q}=\frac{2}{3}$R