The effective resistance between A and B in the given circuit is

The two $3\mathrm{\Omega }$ resistors are in series which will result in one $6\mathrm{\Omega }$ resistor.

And the two $6\mathrm{\Omega }$ resistors in parallel combination will result in $3\mathrm{\Omega }$

And similarly the next steps

This will result in

Final circuit is shown
$\Rightarrow {\mathrm{R}}_{\mathrm{AB}}=\frac{6\times 3}{6+3}=2\mathrm{\Omega }$