If there are two pressure waves (like sound waves) that travel in opposite directions and have the same amplitude then destructive interference occurs: one wave will compress the air particle (here air is the medium) and the second wave will try to rarefact or relax the same air particles with equal pressure. Does it means that net displacement of air particles is zero? then, how is energy getting transferred?
There is no net energy being transferred. The energy each wave has is cancelled by the other wave!
You might be confusing this with the "two slit" experiment. In this case you do have both, destructive and constructive interference. This is the result of two simultaneous waves with a given spatial separation causing the waves to "cancel" each other at some points and "sum" each other at other points.