Initial square wire

The wire is originally in the shape of a square, with resistance of each side: $R_{\text{side}}=3\,\Omega$

Since a square has 4 sides, the total resistance of the whole wire is: $R_{\text{total}}=4\times 3=12\,\Omega$

Wire bent into a complete circle

When this same wire is bent into a circle, its total length and total resistance remain unchanged.

So, the circular wire has total resistance: $12\,\Omega$

Resistance between diametrically opposite points

Diametrically opposite points divide the circle into two equal semicircles.

Therefore, each semicircle has half the total resistance: $R_{\text{semi}}=\frac{12}{2}=6\,\Omega$

Equivalent resistance of the two semicircles

These two semicircles are connected in parallel between the diametrically opposite points.

So the equivalent resistance is: $R_{\text{eq}}=\frac{6\times 6}{6+6} = \frac{36}{12}=3\,\Omega$

Final answer

$\boxed{3}$