Please help me in solving this..?

2Ω // 2Ω --->R of AB = 1Ω
--->
1Ω //2Ω --->R equivalent of AB = (1)(2)/(1+2)=2/3 Ω

Resistors 1 and 1 are in series. They combine for a resistance of 2. Now you have three parallel resistances of 2 each.
1\r = 1\2 + 1\2 + 1\2
R= 2\3