Answer: Option B
Given radii of three metallic spheres be $${r_1},\,{r_2},\,{r_3}$$   are 6 cm, 8 cm and 10 cm respectively
Let the radius of the new sphere be R
$$\eqalign{
& \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi \left( {r_1^3 + r_2^3 + r_3^3} \right) \cr
& \Rightarrow \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi \left( {{6^3} + {8^3} + {{10}^3}} \right) \cr
& \Rightarrow {R^3} = \left( {216 + 512 + 1000} \right) \cr
& \Rightarrow {R^3} = 1728 \cr
& \Rightarrow R = \root 3 \of {12 \times 12 \times 12} \cr
& \Rightarrow R = 12 \cr} $$
∴ Diameter = 24 cm