Measurements of the ³He nuclear spin-spin relaxation time, T₂, have been carried out for commensurate layers of ³He-Ne mixtures adsorbed on hexagonal boron nitride for temperatures 0.2< T <10 K. A temperature independent relaxation is observed at low temperatures and is interpreted in terms of the effective exchange frequencies for ³He particle exchange on the surface. The results show a strong dependence on the fraction of neon in the adsorbed layer. This variation is discussed in terms of a multiple spin exchange model for ³He in a monolayer. The contributions to T₂ from different components of the exchange, 2-spin exchange (J₂), 3-spin exchange (J₃), 4-spin exchange (J₄) and higher exchange permutations depend on the ³He coverage and thus permit the separation of the amplitudes of the different exchange rates, and in particular allow one to deduce the relative strengths of 2-atom and 3-atom exchange where other methods are sensitive only to the effective two-particle term J_eff J₂ - 2J₃.