The process of flame annihilation resulting from downstream interactions of premixed hydrogen-air flames is studied using Direct Numerical Simulations (DNS). The process is investigated during unsteady interaction between a vortex pair and a premixed flame kernel in 2D. The annihilation process results from the interactions of the premixed flames on their products' side. The simulations show that the mechanism of extinction during downstream interaction is different from an upstream interaction, which is governed by the sequence of the interactions of the different preheat and reaction layers on both processes and the diffusive transport of heat and mass. In contrast to observations related to upstream interactions, downstream interactions lead to a shift in the equivalence ratio towards the richer conditions with a steady decrease in chemical activity and no radical pool buildup during the stages of extinction. The effect of vortex sizes is qualitatively the same between the different cases considered.