Is it permissible to commit sins after fasting the Day of Arafah, knowing that it expiates the coming year, and what is your guidance to someone who intends to sin based on this expiation?

It is never permissible to commit a sin, especially after an act of obedience, as that is a sign of abandonment (by Allah). Sins and acts of disobedience have been forbidden in the Qur’an and Sunnah (definition), and the principle is that a good deed should be followed by another good deed, not by an evil one. The fast of Arafah expiates minor sins for two years, but major sins require repentance. As for someone who intends to commit a sin relying on its expiation by fasting, this is wickedness and abandonment (by Allah), and there is no guarantee that their fast will be accepted, especially since a sign of accepted obedience is its continuity. A sin may become a major one through persistence and audacity, and death may come suddenly before repentance.