In Book 6, we see stories about the deaths of two prominent figures, Retired Emperor Takakura and Taira no Kiyomori, so it is fitting to discuss ancient Japanese funeral practices and what the Japanese society at the time thought about death.
In Japan, funerals were handled primarily by Buddhist monks and so the funeral practices were heavily influenced by Buddhism. Since death was considered dirty in Shintoism, getting near or touching dead bodies would make one unclean, the Buddhist monks were left to handle most, if not all, of the work. In many Far East Asian countries, Buddhism is associated with the veneration of the deceased, and in Japan conducting funerals became one of the religion's main functions. This may have caused the "funeral Buddhism" in Japan today, as the religion's main function is conducting prayers and performing rites for the dead [1]. The various sects of Buddhism in Japan have their own specific rituals regarding funerals and prayers for the deceased, but they all have the same goal of honoring those that have passed away.
In the sixth book of The Tale of the Heike we are shown three main traditions that the Japanese of the time practiced. They told eulogy like stories to appease the spirits of the recently deceased, gave gifts to Buddhist temples, and cremated the bodies on funeral pyres. The inclusion of episodes 2-4 and episodes 8-10 immediately after the deaths of Retired Emperor Takakura and Taira no Kiyomori, respectively, serve as examples of the tales shared in order to pacify the recently departed, probably so that they would not return as apparitions. Episode 7, “The Death of Kiyomori,” depicts how his family sent gifts of money and commodities to Buddhist temples when they realized that Kiyomori was dying and it also mentions that he was cremated in true Buddhist fashion "He whose fame had so resounded the whole length and breadth of Japan, who had wielded colossal power, Kiyomori, in an instant floated as smoke into the sky over they city, while the remains mingled soon with the sands of the shore, and all he had been returned to earth." [2]
[1] "Funerary Practices in Japanese and Other Asian Buddhist Societies" Mohan Wijayarat, 1997 http://publications.nichibun.ac.jp/region/d/NSH/series/jare/1997-01-01/s001/s029/pdf/article.pdf
[2] "The Tale of the Heike, Episode 7: The Death of Kiyomori" translated by Royall Tyler, 2012