I have a favour to ask you. My car is being repaired, so I was wondering if you could give me a lift to work tomorrow. I thought because we start at the same time and live in the same neck of the woods (Gegend / Nachbarschaft), it wouldn’t be too much trouble for you.
Originally „neck of the woods“ referred to a narrow stretch of woods or forest. It then took the meaning of a settlement in such an area. This then changed again to mean any area where people live.