Sankata Hara Chaturthi
Sankashti Chaturthi (संकष्टी चतुर्थी) also known as Sankata Hara Chaturthi is an auspicious day dedicated to Lord Ganesha. This day is celebrated in every Lunar month or Hindu calendar month on the fourth day of Krishna Paksha (dark lunar phase or the waning phase)
There are two types of chathurthi. One is sukla patksha chathurthi which comes after New moon day and the other one is krishna patksha chathurthi that comes after Full moon day.
In Krishna patksha chathurthi Lord Ganesha's pooja should be performed in the evening when the moon rises in the sky after keeping upvaas (Fasting) for the whole day. This pooja is completed only after giving arkya to lord Chandra. This is called sankatahara chathurthi pooja. It is believed that the person who does this pooja will get relieved from all their worries and troubles.
Ganapati Atharvasheersha: Before moonlight the Ganapati Atharvasheersha is recited to invoke the blessings of Lord Ganesha.
Angarika Chaturth (अंगारिका चतुर्थी) is a Sankashti Chaturthi falling on Tuesday. It is considered highly auspicious among all Sankashti Chaturthi days.
According to Hindu teachings, Angarak the son of Mother Earth and Bharadwaj Rishi, was an accomplished rishi and a great devotee of Lord Ganesha. He worshipped Lord Ganesha and sought his blessings. On Magh Krishna Chaturthi (the day was Tuesday), Lord Ganesha blessed him and asked him for a wish. Angarak expressed that his only wish was to be associated with Lord Ganesha’s name for forever. The Lord granted his wish and proclaimed that whoever worships Lord Ganesha on Angarika Chaturthi will be granted all that he/ she prays for. From that day onwards, Magh Krishna Chaturthi came to be known as Angarak Chaturthi.