When electric current is passed though two parallel conductors then due to mutual forces between them do they move toward each other. if yes what is the reason behind this?

Two parallel conductors which each carry a current in the SAME DIRECTION will ATTRACT one another, while two such conductors which carry currents in an OPPOSITE DIRECTION will REPEL each other:

Conductor B produces a magnetic field which is perpendicular to the current flow in A.

The force acting on A will be at right angles to the current flow and at right angles to the magnetic field.

Now apply Fleming''s left Hand rule: point the first finger in the direction of the field, the second finger in the direction of the current, and then your thumb will point in the direction of the direction of the force experienced by the conductor A.

A similar argument will show that the field due to conductor A will cause a force on B towards A. Hence the conductors are attracted to each other.