Avalee, I'm not sure what you're asking, but I think you are asking how the pioneers of the church arrived at October 22, 1844 as being the end of the 2300 days rather than the rabbinical Day of Atonement which, in 1844 fell in late September. Bob Pickle has written a paper on this -
http://www.pickle-publishing.com/papers/karaite-reckoning-1844.htm that is a good answer.
In a nutshell, the pioneers looked in the bible on how to interpret the Jewish calendar to determine the date of the Day of Atonement for 1844, and they then corroborated their findings by reviewing the interpretations of the Jews. They found that most Jews did not follow the biblical calender, but that the Karaite Jews did, and that these Jews celebrated the Day of Atonement on October 22 in 1844.