If three metallic spheres of radii 6 cm,

Let r be the radius of single sphere.

Now,

The volume of single sphere = sum of volume of three spheres

$\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi(61)^{3}+\frac{4}{3} \pi(8)^{3}+\frac{4}{3} \pi(10)^{3}$

$r^{3}=1728$

$r=12 \mathrm{~cm}$

Hence, the diameter = 20 × r = 24 cm

Hence, the correct answer is choice (b).