Question

The resistance of each side of equilateral triangle is 6 ohm. Calculate the equivalent resistance between end of a side.

Answer 1

Do not be under the impression that it is only 2 ohm, because A and C are also connected to each other through the route of B. So, the resistance along that route must also be considered.
Resistance along path 1 (A---->C) = 2 ohm
Resistance along path 2 (A-->B-->C) = 2+2 = 4 ohm, as both the 2 ohm resistors are in a series connection.
Now both these paths are in parallel (any two paths are in parallel when both their end points are the same, or at the same potential).
So, we have the final resistance between A and C as = 2 || 4 = 2*4/(2+4) = 1.33 ohm.

hope it helps to you.