Taking the four vertices of a square as centres, four circles of equal diameter are drawn in such a way that each circle touches two other circles, as shown in the figure below :

The correct answer is (b) 4.0 cm.

The diameter of each circle is 4 cm, and the radius of each circle is 2 cm. The centers of the four circles are located at the four vertices of a square. The distance between any two adjacent vertices of a square is 2√2 cm. Therefore, the distance between the centers of any two adjacent circles is 2√2 + 2 = 4 cm.

The following figure shows a diagram of the four circles with their centers at the four vertices of a square. The dashed lines represent the radii of the circles.

[asy]
unitsize(1 cm);

draw((0,0)–(2,0)–(2,2)–(0,2)–cycle);
draw((0,0)–(1,1));
draw((1,0)–(2,1));
draw((2,0)–(1,1));

draw((0,0) circle(2 cm);
draw((1,0) circle(2 cm);
draw((2,0) circle(2 cm);
draw((0,2) circle(2 cm));
[/asy]

Each circle touches two other circles. The two circles that touch a given circle are the circles that are adjacent to the given circle in the square. Therefore, the distance between the centers of any two adjacent circles is 4 cm.