Answer
reduces by $
\dfrac{1}{4} \text{ times}
$
Work Step by Step
The variation model described by the problem is $
I=\dfrac{k}{d^2}
,$ where $I$ is the intensity of light and $d$ is the distance from the light source.
Substituting $d=12$ in the equation above results to
\begin{array}{l}\require{cancel}
I=\dfrac{k}{12^2}
\\\\
I=\dfrac{k}{144}
.\end{array}
Substituting $d=24$ in the equation above results to
\begin{array}{l}\require{cancel}
I=\dfrac{k}{24^2}
\\\\
I=\dfrac{k}{576}
.\end{array}
Hence, when $d=24$ (doubled), the intensity of the light reduces by $
\dfrac{1}{4} \text{ times}
.$
