Solution:

\begin{aligned} & L_{1} : 3 x+2 y-5=0 \quad \text { and } \quad L_{2} : 6 x+4 y-6=0 \ \therefore L_{1} : 6 x+4 y-10=0 & \text { and } \quad L_{2} : 6 x+4 y-6=0 \ \therefore \quad a=6 &, \quad b=4 \quad, \quad c_{1}=-10 \quad \text { and } \quad c_{2}=-6 \end{aligned}

\begin{aligned} d &=\left|\frac{c_{2}-c_{1}}{\sqrt{a^{2}+b^{2}}}\right| \ &=\left|\frac{-6+10}{\sqrt{6^{2}+4^{2}}}\right| \ &=\left|\frac{4}{\sqrt{52}}\right| \ &=0.555 \quad \text { or } \quad \frac{2}{\sqrt{13}} \end{aligned}