A freshly prepared radioactive source of half life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is:

The radioactivity of a sample decreases to $\left(\frac{1}{2^{\mathrm{n}}}\right)$ after n half lives. Since the initial activity is 64 times the permissible level, it must become ${\left(\frac{1}{64}\right)}^{\mathrm{th}}$of its initial value.

$$\begin{gathered} \therefore \frac{1}{64}=\frac{1}{2^{\mathrm{n}}} \\ \Rightarrow n=6 \end{gathered}$$

In other words, after six half- lives the activity will reduce itself to the permissible level. 
Since half-life is 2 hours, the total time taken = 2 x 6 h = 12 hours.