Motivated by a hint in a CMS search for right-handed $W$-bosons in $eejj$ final states, we propose an experimental test of quark-mixing matrices in a general left-right symmetric model, based on counting the numbers of $b$-tags from right-handed $W$-boson hadronic decays. We find that, with our test, differences between left- and right-handed quark-mixing matrices could be detected at the LHC with $\sqrt{s}=14$ TeV. With an integrated luminosity of about $20/\textrm{fb}$, our test is sensitive to right-handed quark-mixing angles as small as about $30^\circ$ and with $3000/\textrm{fb}$, our test's sensitivity improves to right-handed mixing angles as small as about $7.5^\circ$. Our test's sensitivity might be further enhanced by tuning $b$-tagging efficiency against purity.