Answer
15 hours.
Work Step by Step
$2.0\,\mu g=16\,\mu g\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$
$16\,\mu g$ decays to $2.0\,\mu g$ in 3 half-lives.
$\implies 3.0\,\text{half-lives}=45\,\text{hours}$
Or half-life $t_{1/2}=\frac{45\,hours}{3.0}=15\,hours$