A newly prepared radioactive source with a half-life of 2 h emits...

Let the safe level of radiation intensity be $I_0$.

The initial intensity of the radioactive source is $I = 64 I_0$.

The intensity after $n$ half-lives is given by $I(t) = I \left(\dfrac{1}{2}\right)^n$.

For the source to be safe to work with, we require $I(t) \le I_0$.

$64 I_0 \left(\dfrac{1}{2}\right)^n \le I_0$

$\dfrac{64}{2^n} \le 1$

$2^n \ge 64$

Since $64 = 2^6$, we get $n = 6$.

The minimum number of half-lives required is $6$.

Given the half-life $T_{1/2} = 2 \text{ h}$, the minimum time required is $t = n \times T_{1/2} = 6 \times 2 \text{ h} = 12 \text{ h}$.