The equivalent resistance between the points A and B in the...

Using Kirchhoff's laws on the bridge circuit with resistances $6\Omega, 3\Omega, 3\Omega, 3\Omega, 6\Omega$ and applying a 1V test voltage:

From the loop equation:
$6i_1 + 3(2i_1 - i) = 3(i - i_1)$

$15i_1 = 6i \Rightarrow i_1 = \frac{2}{5}i$ ...(1)

From the second loop:
$3(i - i_1) + 6i_1 = 1$
$3i + 3i_1 = 1$

\left(3 + \frac{6}{5}\right)i = 1$<br><br>$i = \frac{5}{21} A = \frac{1V}{R_{eq}}$<br><br>$R_{eq} = \frac{21}{5} = 4.2 \ \Omega