Question

a in the circuit shown the equivalent resistance between a and b is

Answer 1

see 
here point 1 connected to point 3 and point 3 connect to point 6 directly so therefore point 1 connected to point 6 and so that's why this a zero potential point from 1 to 6 ...so remain 6 to B point has only one R resistance so 

net resistance between A and B is R 

i hope it will help you 
regards

Answer 2

Equivalent resistance between a and b in the circuit is $\frac{R}{3}$.

Explanation:

First take the two resistances which are in series to each other in between.

         

                      ⇒ R + R = 2R

               Do the same for another pair in between.

Now, take the left pair which is inside and made a parallel connection with most left resistance.

                 ⇒ $\frac{1}{2R} + \frac{1}{2R} = \frac{3}{2R}$

    Now, again take parallel with right inside to the above one.

                        ⇒ $\frac{2}{3R} + \frac{1}{2R} = \frac{2}{R}$

   

        Now the parallel combination is left. Now, take the parallel combination.

                           ⇒    $\frac{2}{R} + \frac{1}{R} = \frac{3}{R}$

       So,  $\frac{R}{3}$ is the equivalent resistance.