The correct answer is: a) Parashurama.
The Kalika Purana is a Hindu text that associates the region of Arunachal Pradesh with the legend of Parashurama. According to the legend, Parashurama was a warrior who was born to kill the king of the Kshatriyas, Kartavirya Arjuna. Parashurama killed Kartavirya Arjuna and then went on to perform a penance in the Himalayas. During his penance, he was visited by the goddess Durga, who gave him a boon. The boon allowed Parashurama to create a new land for himself, which he named Arunachal Pradesh.
The other options are incorrect because they are not associated with the legend of Parashurama. Rukmini was the wife of Krishna, Bhishmaka was the father of Rukmini, and Ghatotkacha was the son of Bhima and Hidimba.