A newly discovered novel frustrated antiferromagnets Li3Mg2MO6 (M = Ru, Os) constitutes edge-sharing triangles of M4+ ions (S = 3/2) linked by corner-sharing in the ab-plane. The M spins interact with each other via four different antiferromagnetic exchange interactions, J1, J2, J3 and J4. Despite the considerable geometrical frustration, Li3Mg2MO6 exhibits an antiferromagnetic long-range order at TN = 18 K for M = Ru and TN = 8 K for M = Os. Heat capacity and neutron diffraction results also show the development of short-range spin correlations well above TN for both compounds. All of the experimental results render Li3Mg2MO6 an intriguing platform to study the combined effects of geometrical frustration, complex energy hierarchy, and spin-orbit couplings. With the aid of inelastic neutron scattering, we can unveil the spin dynamics of Li3Mg2MO6 and complex energy hierarchy therein.