We consider the effects of a quench to T = 0 on a spin system with axial next-next nearest neighbour Ising interactions, evolving under a conserved 3-spin flip dynamics. Such a model is motivated by the kinetics of stacking layers in polytypes near the 3C-6H transition. We find that the system generically gets arrested in interesting metastable states which have inhomogeneously distributed quiescent and active regions. In such arrested states, the autocorrelation function decays as a stretched exponential $sim exp(-(t/tau_{o})^{1 over 3})$. The latter feature can be understood in terms of a mapping of the dynamics within active stretches to the well known simple exclusion process of particles on a line, and bounds can be put on $tau_o$.
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