If coefficient of $x$ and $y$ of both the lines are same, then the lines are parallel
Given equation of lines are
$3x + 4y = 9 \quad…(i)$
and $6x + 8y = 15$
$\Rightarrow 3x+4y=\frac{15}{2}\quad\ldots\left(ii\right)$
$\therefore $ Both lines are parallel, therefore the distance between two lines
$=\frac{\left|\frac{15}{2}-9\right|}{\sqrt{3^{2}+4^{2}}}$
$=\frac{\left|15-18\right|}{2\sqrt{25}}=\frac{3}{2.5}=\frac{3}{10}$ Alternative The perpendicular distance from origin to the line $L_1$ is
$d_{1}=\frac{9}{\sqrt{3^{2}+4^{2}}}=\frac{9}{5}$
and $d_{2}=\frac{2}{\sqrt{3^{2}+4^{2}}}$
$=\frac{15}{2\cdot 5}=\frac{15}{10}$
$\therefore $ Distance between $L_{1}$ and $L_{2}$ is
$d=d_{1}-d_{2}$
$=\frac{9}{5}-\frac{15}{10}=\frac{18+15}{10}$
$=\frac{3}{10}$
