  A foremost task in understanding the nature of the $X(3872)$ involves the
discrimination of the two-quark and multiquark configurations. In this work, we
propose a method to probe the short-distance component of the $X(3872)$ by
measuring the ratio between the $B_c$ semileptonic and nonleptonic decays into
the $X(3872)$. We demonstrate that if the $X(3872)$ production mechanism is
through the $\bar cc$ component, the ratios would be universal and could be
reliably predicted in theory. Measurements of these ratios at LHC and the
next-generation electron-positron colliders are capable of
validating/invalidating this production mechanism and providing deeper insights
into the nature of the $X(3872)$.
