6 days is 144 hours, and since (physiologically) no hen can lay more than one egg every 26 hours, there is no way you can get more than 27 eggs.
Yes, you can get one egg a day from a hen, for a few days. If the hen lays at 8 am one day, ten the next, and noon the third, on the 2 pm on the fourth, and the next she will not lay. (Chickens do not lay eggs in the very late afternoon or middle of the night. If you live above the arctic circle in the winter I have no idea what your poor chickens much go through.)
Source: I asked one of my chickens. (She is really helpful with these types of questions)