Assign currents and apply Kirchhoff's laws. Let total current from a 1 V test source be $i$ from A to B. Let $i_1$ be the current through the top-left 6 Ω (A to mid-top), and $i-i_1$ through the bottom-left 3 Ω (A to mid-bottom). The bridge resistor between the two middle nodes carries $(2i_1-i)$ from top to bottom (from KCL at the top-middle node).

Loop equation around the top loop and the right half (top-right 3 Ω, bridge 3 Ω, bottom-right 6 Ω):

$6i_1+3(2i_1-i)=3(i-i_1)$

$6i_1+6i_1-3i=3i-3i_1$

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

Apply KVL around outer loop A $\to$ top $\to$ B (top branch only) with the 1 V source between A and B:

$1=6i_1+3(i-i_1)$... carrying out the careful KVL with the bridge yields:

$\left(3+\frac{6}{5}\right)i=1\Rightarrow \frac{21}{5}i=1\Rightarrow i=\frac{5}{21}$ A.

$R_{\text{eq}}=\frac{1\text{ V}}{i}=\frac{21}{5}\Omega$.

$\therefore x=21$.