Two ways you can demonstrate know-how on a job interview when someone asks you a question about how you would solve a problem:

1. You can quickly offer up the first answer that pops into your head.

2. Ask any important clarifying questions related to the problem, then offer your solution.

In my experience, people who are truly masters of their own domain are inclined more towards the second approach. It's naive to jump right to the assumption that you fully understand the problem right away. Much better to use the divide-and-conquer strategy, and figure out exactly where the problem lies.