Percy, the main character of the story, is rushed out of his home by his mother and best friend Grover. Grover turns out to be a satyr, half goat half man. Percy does not yet know what is going on or why he must leave but he decides to trust his loved ones and leave. This is his call to adventure and he willing accepts the call.
Percy is rushed to Camp Half Blood, while being chased by a Minotaur. Percy has to face the Minotaur when it grabs his mom. Percy is not in time to save her, but he ends up killing the Minotaur in the end by ripping off its horn. This is an emotional and physical challenge for Percy because he is terrified and sad after his mother dies. He completes both of these steps at great cost to himself.
Percy enters Camp Half Blood with the Minotaur's horn in hand. He enters very confused and stunned after what has happened. He crosses the threshold because his mother told him that this was the only place he would be safe. Percy completes this step in the Hero's Journey in honor of his mother.