I am still not sure how to answer
Well, what will you try to accomplish in your first few months? Do you expect to be using that time learning the existing systems? Do you intend to spend the time building relationships? Will you try and ensure that the team is following modern best-practises? Will you keep your head down and get the lay of the land?
What I'm trying to get at here is that the way to answer this question (and all interview questions) is honestly. If you answer honestly about your intentions and they don't like it, then you wouldn't have had a good time at the job anyway.
If you're not sure what your intentions are then just say that, and follow up with your reasoning about why you're not sure yet and the broad outlines of what you'd do to determine what you'd like to accomplish when you've learned more about the job and/or workplace.
In response to your edit about being more clear and concise:
A technique I like to use is to give a brief one sentence "executive summary" at the start, then go into more detail about what I mean. If you need time to think before you have a clear summary ready then say that, maybe with a compliment about the question. So (I'm trying to guess at your intentions based on what you wrote in your edit) something like
Wow, good question... I'm not sure yet. When I join a new team I like to start by learning about the tasks I'll be performing, and I've found that the best way to do that varies at different companies. So I expect I'll spend my time learning the appropriate ways to get up to speed, and getting more in depth knowledge of the tasks I'll be performing and the best way to perform them.
I'm not suggesting that this is a perfect answer (or the one that I'd give, or you should have given), but it' an example of the structure I'd use in an answer of my own.