Let, the equation of the line is $\frac{x}{a}+\frac{y}{b}=1\Rightarrow \frac{2}{a}+\frac{2}{b}=1$
$\Rightarrow 2\left(b+a\right)=ab\dots .\left(\mathrm{i}\right)$
Case I: If both intercepts are positive
Then, $\frac{1}{2}ab=4\Rightarrow ab=8\Rightarrow b+a=4$
$\Rightarrow a\left(4-a\right)8\Rightarrow a^2-4a+8=0$
$\Rightarrow$ No $‘a’$ is possible (Discriminant is negative)
Case II: If intercept are of opposite sign, then $-\frac{1}{2}ab=4\Rightarrow ab=-8$
$\Rightarrow b+a=\frac{-8}{2}=-4\Rightarrow a^2+b^2=16-2\left(-8\right)=32$
$\Rightarrow$ the distance of origin from the line is $\frac{\left|ab\right|}{\sqrt{a^2+b^2}}=\frac{8}{\sqrt{32}}=\sqrt{2}$ units