Answer
The charged particle should be placed in between them
Work Step by Step
The left charge(q1) is experiencing a force to the left
And the right charge (q2) is experiencing a force to the right
For there to be an equilibrium when adding a charged particle it has to cancel the forces acting on q1 and q2.
To do this it will have to create an electrostatic force on q1 towards the right
and would have to create an electrostatic force on q2 towards the left
This would be achievable by putting the charge in the middle
