Final answer:
Poseidon's intervention on behalf of Aeneas in Book 20 is likely due to a connection to divine and heroic figures, potentially upholding a divine promise. The correct option is C, by a process of elimination and understanding of mythical themes, to fulfill a promise to Aeneas's father.
Step-by-step explanation:
The question refers to a specific event in classical literature, particularly concerning the character Poseidon (Neptune in Roman mythology) and his intervention on behalf of Aeneas.
In the context of Book 20, this intervention is not related to Poseidon trying to save Aeneas from drowning, preventing Aeneas from winning a battle, or pleasing Hera. Instead, Poseidon's intervention can be attributed to his connection to the divine and heroic figures of the mythology, similar to the instances of divine interventions seen in the narratives of heroes like Perseus in their respective myths.
The story provided about Poseidon's punishment of Queen Cassiopeia suggests that Poseidon, who is often involved in human affairs, acts in a manner that maintains the natural order and sometimes upholds familial or divine promises. In the case of Aeneas, it is plausible that Poseidon intervened due to a promise or obligation towards Aeneas's father, Anchises, with whom he may have had a connection, as ancient deities often did.
However, it's important to note that the story explicitly mentioning Poseidon's promise to Anchises in Book 20 is unavailable, thus leaving us with an educated deduction based on the understanding of mythological patterns. The correct option, based on deductive reasoning and an understanding of mythological themes, is (c) To fulfill a promise to Aeneas's father.