Sankashti Chaturthi is the fourth tithi of Krishna Paksha, observed every month as a fast for Ganesha, the remover of obstacles (sankata). When it falls on a Tuesday it is called Angaraki Chaturthi and is considered especially auspicious.
The fast lasts from sunrise until the Moon is sighted in the evening; devotees offer arghya to the Moon and then break the fast. Because the moonrise matters, the date is fixed by the Chaturthi tithi prevailing at moonrise.