What is Gilgamesh trying to accomplish in Chapter 6 +7, what is he looking for?

Gilgamesh humiliates a goddess by refusing to marry her. This causes the goddess to send the Bull of Heaven to destroy Uruk and kill Gilgamesh, but she underestimates Enkidu. Enkidu holds down the bull while Gilgamesh kills it. Full of pride, Gilgamesh brags, causing the gods to become angry. They decide one of them needs to die. Enkidu is the one who is chosen to die.

Gilgamesh adores his friend, who is the first person he has known that he can consider an equal. When Gilgamesh learns that Enkidu is dying, he becomes very upset. If not for Enkidu, Gilgamesh might not have killed Humbaba or been able to kill the Bull of Heaven. For this reason, the reader wonders what will happen to Gilgamesh once Enkidu is gone.