jmc

If the diameter of the circle is $16$, then its radius is $8$. The area of this circle is then $\pi r^2=\pi (8^2)=64\pi$. If we want the area of the new circle to be $48\pi$ less than the area of this one, then the new circle must have an area of $64\pi -48\pi =16\pi$. Now that we know the area of this circle, we can find its radius $R$ by setting $\pi R^2$ equal to $16\pi$, so we have that $\pi R^2=16\pi$ and $R=4$.

The radius of the first circle was $8$ and the new radius is $4$, so the radius was decreased by $8-4=\boxed{4}$.