Official solution
Solving lines \[\mathrm{L}_1(3 \mathrm{x}+2 \mathrm{y}=14)\] and \[\mathrm{L}_2(5 \mathrm{x}-\mathrm{y}=6)\] to get \[\mathrm{A}(2,4)\] and solving lines \[\mathrm{L}_3(4 \mathrm{x}+3 \mathrm{y}=8)\] and \[\mathrm{L}_4(6 \mathrm{x}+\mathrm{y}=5)\] to get \[\mathrm{B}\left(\frac{1}{2}, 2\right)\].
Finding Eqn. of \[\mathrm{AB}: 4 \mathrm{x}-3 \mathrm{y}+4=0\]
Calculate distance PM
\[\Rightarrow\left|\frac{4(5)-3(-2)+4}{5}\right|=6\]