Question

A pair of girls trying to pull each other.both ar applying force and how

Answer 1

When the two girls are trying to pull each other, both will be applying an opposite force on each other.
The force they apply on each other, if non of them is moving, is equal and are cancelling out each other. This makes the net force or the resultant force to be zero. 
The resultant force is the resulting magnitude of two or more forces acting on an object and will take the direction of the net resulting force. Hence, if the net force is zero, non will move but if one of the two girls exerts a larger force, the other girl will move towards her to the direction of the resulting force.