According to the ancient texts, the great oath of the gods could be sworn either by bowing your head or by the waters of the Styx.
What Zeus says in the fourth panel is inspired by a phrase in the Iliad. When Hera asks Aphrodite for a favour, she responds: "Speak whatever is in your mind. My heart is urgent to do it if I can, and if it is a thing that can be accomplished". I think Hephaistos says the same when Thetis comes and asks him for a favour.