$\begin{align}
& I=\frac{{\bar{P}}}{A}=\frac{{\bar{P}}}{4\pi {{r}^{2}}}\Rightarrow \frac{{{I}_{2}}}{{{I}_{1}}}={{(\frac{{{r}_{1}}}{{{r}_{2}}})}^{2}}\Rightarrow \frac{{{I}_{2}}}{{{I}_{1}}}={{(\frac{1}{4})}^{2}}=\frac{1}{16} \\
& \left\{ \begin{matrix}
{{\beta }_{1}}=(10dB)\log \frac{{{I}_{1}}}{{{I}_{\circ }}} \\
{{\beta }_{2}}=(10dB)\log \frac{{{I}_{2}}}{{{I}_{\circ }}} \\
\end{matrix} \right.\Rightarrow \Delta \beta ={{\beta }_{2}}-{{\beta }_{1}}=(10dB)\log \frac{{{I}_{2}}}{{{I}_{1}}} \end{align}$
$\Rightarrow \Delta \beta =(10dB)\log \frac{1}{16}\Rightarrow \Delta \beta =10dB(\log 1-\log {{2}^{4}})=(-40dB)\log 2=-40\times 0/3=-12dB \\
$