We live in a fast paced era. To solve a problem is one thing, but to solve it quickly is another one. Interviewers try to recruit desktop support technicians with an ability to analyze the problem quickly, design a solution and apply it.
What more, this question hides several other traps. It is a two part question (identifying the situation is a first part and describing your solution is a second one). Good listener, that means good applicant for the job, will answer both parts.
It is a behavioral question too. You should speak about a situation from the past. Interviewer sees what you consider to be a difficult problem. Based on that they can easily assess your true level of experience and knowledge.
Choose a difficult problem you solved
Obviously, you should always pick a problem you solved, ideally one you solved in a short time. When speaking about it, do not forget to stress the impact the problem had on the daily operations of the office. Try to speak clearly and to the point, describing a solution in a simple way.
What if you have no desktop support experience?
Behavioral questions are very difficult for people with little or no working experience. However, as you can see in the question, they do not specify a problem you should talk about. They only inquire about a quick solution to the problem. So, if this is your first job application, or if you simply haven’t solved any difficult problem related to SW or HW in the past, you can calmly talk about something that is not related to this job. Your attitude and communication skills matter, not the exact problem.
You can find countless descriptions of computer-related problems on the web. You can research it and think up an imaginary situation before an interview. This is a good alternative for people without experience.
Note: I know it means to lie. And we should never lie… But each of us has to start one day and job interviews are sometimes not fair to people without experience. So in this case, a little lie is acceptable.