In this study, the thermal conductivity properties of the tetrahedrite-structures compound Ag6Si6Sn4P12, whose phonon properties have not been reported so far, are investigated in depth using self-consistent phonon calculations that consider up to fourth-order anharmonic terms. Compared to the previously studied Ag6Ge10P12, a tetrahedrite-manner phosphide, Ag6Si6Sn4P12 without lone pairs, has a unique feature in that it exhibits softening of the Ag and Sn phonon modes at 300 K and has a short phonon lifetime owing to its relatively high anharmonicity. This is believed to be the cause of the extremely low lattice thermal conductivity of Ag6Si6Sn4P12. Additionally, we also observed a nonnegligible contribution of the coherent component to the thermal conductivity of Ag6Si6Sn4P12 because of its wide phonon linewidth, suggesting that Ag6Si6Sn4P12 exhibits glass-like phonon transport properties.