The number of balls of radius $2\text{cm}$ that can be made from a solid sphere of radius $4\text{cm}$ is:

The volume of a solid sphere of radius $R$ is given by:
$$V=\frac{4}{3}\pi R^3$$
Let $R=4\text{cm}$ be the radius of the large sphere, and $r=2\text{cm}$ be the radius of the smaller balls.The number of small balls $n$ that can be formed is equal to the ratio of the volumes:
$$n=\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}={\left(\frac{R}{r}\right)}^3$$
Substituting the values:
$$n={\left(\frac{4}{2}\right)}^3=(2{)}^3=8$$