Kartika shukla vidiya is the second day of kartika masa, also called as Yama dwitiya, Bhratri dwitiya. It is a good festival, the main rituals to be followed on this day are, worshiping Lord Yama along with Chitragupta and Bhagini gruha bojana(taking meals in sisters house).
A story is in vogue about this day,
Yamuna river is the sister of Lord Yama. Yamuna invited her brother to her house many times. But Lord Yama was unable to go to his sister's house. At last he went to his sister's house. That day is kartika suddha vidiya. Yamuna showed great respect to her brother, his parivara and worshipped Lord Yama. She herself prepared food and offered to all of them.
Lord Yama was very much pleased,asked her to choose a boon. Then Yamuna asked a boon that on this day, "The brother who goes to his sister's house and takes food from her, will never go to Naraka and sudden ďeath". Lord Yama agreed and also said that, "The sister who invites her brother and serves food to him on this day, will never become widow".
In honour of Lord Yama this day is popular as Yama dwitiya. The main ritual on this day is worshipping of brothers by sisters, so it is also called as Bhratri dwitiya.
In the evening, people worship Moon God and King Bali on the occasion of his return to Patala lokha