  Hyperfine-changing collisions are of fundamental interest for the studying of
ultracold heteronuclear mixtures. Here, we report the state-to-state study of
the hyperfine-changing-collision dynamics in a Bose-Fermi mixture of $^6$Li and
$^{41}$K atoms. The collision products are directly observed and the
spin-changing dynamics is measured. Based on a two-body collision model, the
experimental results are simultaneously fitted from which the spin-changing
rate coefficient of $ 1.9(2)\times 10^{-12}~\rm{cm^3\cdot s^{-1}}$ is gained,
being consistent with the multi-channel quantum defect theory calculation. We
further show that the contact parameter of $^6$Li-$^{41}$K mixture can be
extracted from the measured spin-changing dynamics. The obtained results are
consistent with the first order perturbation theory in the weakly-interacting
limit. Our system offers great promise for studying spin-changing interactions
in heteronuclear mixtures.

Quantum Gases;Atomic Physics