See figure attached from problem statement.
The Attempt at a Solution
I've never really done a question of this type so I'm slow to get going.
I'm not sure what is happening when he touches the spheres with the others.
He first touches C to A:
They are postively charged so they should be in repulsion. Is there any exchange of charge or something happening here?
He then touches C to B:
C is postively charged while B is negatively charged so they should attract fairly well. Again, is there some sort of exchange in charge happening here when they touch?
What is happening when the spheres make contact!?
Once I understand this I will worry about trying to find the electrostatic force between spheres A and B.