The equivalent resistance between A   and   B is _______. .

Point D and G are at same potential. Same is the case with point E and F.

Now, resistance between DC and GC are in parallel combination. Similarly, resistance between CE and CF are in parallel combination. The modified circuit will be as shown below considering $R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$ for parallel combination.

Therefore, we can write

$\frac{1}{R_{eq}}=\frac{1}{2}+\frac{1}{12}+\frac{1}{4}+\frac{1}{6}+\frac{1}{2}$

$$\begin{gathered} =\frac{6+1+3+2+6}{12} \\ =\frac{3}{2} \end{gathered}$$

$\Rightarrow R_{eq}=\frac{2}{3}\Omega$