The Ashkenazim start saying Selichos a minimum of 4 days before Rosh HaShana? What is the reason of a minimum of 4 days?
The Mishnah Berurah (OC 581:5) explains: many people have the custom to fast for ten days (including Yom Kippur) as part of seeking repentance (Levush). Starting from Rosh haShannah you lose at least four days: the two days of Rosh haShannah, Shabbat Shuvah (the Shabbat in between Rosh haShannah and Yom Kipppur) and the day before Yom Kippur (when it is forbidden to fast). Thus, the fasting would precede Rosh haShannah by at least four days. And the selichot would be done on days when you are fasting (another custom).
A second explanation from the Mishnah Berurah: animals offered for sacrifice in the temple needed verification that they were free of blemishes for four days before they were offered. And on Rosh haShannah it says ועשיתם עולה (instead of והקרבתם עולה, which it says by all the other sacrifices) from which we learn that a person should consider themselves to be like a korban olah on Rosh haShannah. Thus we begin our spiritual introspection at least four days prior.