A wire has resistance 12 $\mathrm{\Omega }$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to

When wire is bent in the form of a circle, then between two points in any diameter, it is equivalent to two resistances in parallel,  $R_{\mathrm{eq}}=\frac{12/2}{2}=3\Omega$