We report a study of the anharmonic lattice dynamics in low lattice thermal conductivity (κ_{l}) material AgCrSe_{2} by many-body perturbation theory. We demonstrate surprisingly giant four-phonon scattering exclusive for the heat-carrying transverse acoustic phonons due to large quartic anharmonicity and nondispersive phonon band structure, which lead to four-phonon Fermi resonance and breaks the classical τ^{-1}∼ω^{m}T^{n} relation for phonon-phonon interactions. This strong resonant scattering extends over the Brillouin zone and substantially suppresses the thermal transport, even down to a low temperature of 100 K. The present results provide fundamental insights into the four-phonon resonant dynamics in the low-κ_{l} system with flat phonon dispersions, i.e., cuprous halides and skutterudites.