  Inspired by the recent discovery of the $X(6900)$ meson at {\tt LHCb}
experiment, we investigate the inclusive production rate of the $C$-odd
fully-charmed tetraquarks associated with light hadrons at the $B$ factory
within the nonrelativistic QCD (NRQCD) factorization framework. The
short-distance coefficient is computed at lowest order in velocity and
$\alpha_s$. Employing the diquark-antidiquark model to roughly estimate the
long-distance NRQCD matrix elements, we predict the rate for inclusive
production of the $1^{+-}$ $T_{4c}$ state and discuss the observation prospects
at {\tt Belle 2} experiment.
