How can an administrator handle a conflict situation?

An administrator can handle the conflict by 1.
Awareness and understanding about his job.
2.
Awareness and understanding about the company policies and procedures that regulates and operates the company.
Master the 2 things mentioned above.
This way you are strong and confident to provide solution plus using your creative talent and sharp common sense.
We can’t work like blinds.
If we can’t see, we will stumble.
Unawareness AND lack of knowledge about the first two MAKES ALL THINGS CONFLICT IN THE COMPANY, AND WORS EFFECT IS BUSINESS FAILURE.

When interpersonal conflicts arise, apply this seven-step process to resolve them: 1.Talk about the disagreement and agree on the real issue.
2.Ask why the issue is a problem, and why you need to resolve it.
3.Devise several solutions that could resolve the issue.
4.Choose the best solution to the problem, but be willing to compromise.
5.Agree what you each need to do to solve the conflict.
6.Bring closure by shaking hands, repeating your individual commitments and saying “thanks.” 7.Follow through on your commitments.
http://www.businessmanagementdaily.com/6367/7-steps-to-conflict-resolution

Answer is simple in one word. Only communicate regularly you will find your solution sooner or later.