  Recently, first principle-based prediction of lattice thermal conductivity
$\kappa$ from the perturbation theory has achieved significant success.
However, it only includes three-phonon scattering due to the assumption that
four-phonon and higher-order processes are generally unimportant. Also,
directly evaluating the scattering rates of four-phonon and higher-order
processes has been a long-standing challenge. In this work, however, we have
developed a formalism to explicitly determine quantum mechanical scattering
probability matrices for four-phonon scattering in the full Brillouin Zone, and
by mitigating the computational challenge we have directly calculated
four-phonon scattering rates. We find that four-phonon scattering rates are
comparable to three-phonon scattering rates at medium and high temperatures,
and they increase quadratically with temperature. As a consequence, $\kappa$ of
Lennard-Jones argon is reduced by more than 60% at 80 K when four-phonon
scattering is included. Also, in less anharmonic materials -- diamond, silicon,
and germanium, $\kappa$ is still reduced considerably at high temperature by
four-phonon scattering. Also, the thermal conductivity of optical phonons is
dominated by the fourth and higher orders phonon scattering even at low
temperature.
