In many fanfictions where Draco saves Hermione from Greyback, it often starts with a situation where Hermione is in immediate danger from Greyback. Draco, perhaps having a change of heart from his Slytherin ways, decides to intervene. He might use his knowledge of the Death Eaters' plans or the layout of the area to his advantage. For example, he could lead Hermione to a secret passage that Greyback doesn't know about. This event can be a turning point in their relationship, leading to a newfound respect and sometimes even the start of a romantic connection between them, as they both realize there is more to each other than they initially thought.
Ron might use his Weasley family's unique magic items to save Hermione. For example, if he had a special charm from his mother that could repel dark creatures like Greyback. He just needs to activate it at the right moment when Greyback is closing in on Hermione.
There's a fanfiction called 'Greyback's Redemption Arc'. In it, Fenrir Greyback saves Hermione from a group of Death Eaters. The author might have written it to explore the idea of redemption for a character like Greyback. Maybe he saves Hermione because he sees her as a symbol of the good in the wizarding world that he has lost touch with, and this act of saving her could be the start of his journey towards redemption.
One possible motivation is a sense of morality that Draco has buried deep inside. Despite his upbringing in a family of Death Eaters, he still has a conscience. Seeing Greyback about to harm Hermione, who is essentially an innocent in the face of such a brutal werewolf, stirs that conscience. Another factor could be his own self - interest. He might realize that by saving Hermione, he could gain some sort of leverage or protection in the complex world of the wizarding war.
One possible scenario could be that Ron uses his quick thinking and a powerful spell to stun Greyback just as he's about to attack Hermione. Ron might have been lurking in the shadows, waiting for the perfect moment to strike and save his friend.
One possible plot could be that Hermione stumbles upon Fenrir Greyback in a situation where he's about to be killed by some dark wizards who see him as a loose end. Hermione, being the empathetic and brave witch she is, decides to save him. Maybe she believes that every life is worth saving, even a werewolf like Fenrir. She could then try to rehabilitate him, using her vast knowledge of magic and her strong moral compass.
Draco might be motivated by jealousy. He could be jealous of Ron and Hermione's friendship or a possible romantic relationship between them. So he tries to harm Hermione out of spite.
Well, perhaps Snape uses his position as a teacher to step in. He could have been observing the situation secretly and when Draco was about to do something harmful to Hermione, Snape intervened with a firm command or some magic spell to stop Draco in his tracks.
One possible motivation could be that Draco has changed. He might have seen the error of his ways and decided to do the right thing. Another motivation could be that he has feelings for Hermione, even if they are not fully realized yet. He doesn't want to see her in a bad situation, so he steps in.