She might be required to research in the restricted section of the library. Given her penchant for knowledge and Snape's often - dark and esoteric interests, the restricted section could hold the key to whatever he needs help with.
Another task could be assisting Snape in some magical experiments. This could involve handling dangerous magical artifacts, recording data accurately, or even coming up with creative solutions when the experiments go wrong, based on her quick thinking and extensive knowledge.
One possible reason could be related to a difficult potion she's trying to brew. Snape is a potions master, and Hermione might be facing an ingredient or a process that she can't figure out on her own. For example, a rare potion that requires precise handling of dangerous ingredients.
He could also be a bit sarcastic in his response. Snape has a sharp tongue, so he might say something like 'Miss Granger, what makes you think I have the time or inclination to help you?' But as Hermione explains her situation, he might gradually soften, realizing the seriousness of the matter. Maybe he starts to see a bit of himself in Hermione's thirst for knowledge.
Maybe Snape is involved in some sort of mystery or danger within Hogwarts that has to do with magic spells. Hermione, with her vast knowledge of spells and her in - depth study of the Hogwarts library, could be a great help to him in deciphering old spells or magical texts related to the situation.
Maybe Snape has a difficult spell he can't seem to master, and as much as he hates to admit it, Hermione's academic prowess makes her the best person to ask for help. He approaches her in a very snarky way, but she sees through his facade and decides to assist him. This could lead to an interesting dynamic where they start to respect each other more.
Snape would probably be very cold and indifferent at first. He might even think it's some sort of Gryffindor ploy to get his attention or make him look bad. He has always had a low opinion of Hermione's house, so his initial reaction would be guarded.
Perhaps Hermione is injured in a fight against dark wizards while on a secret mission. Snape discovers her and, despite their past differences, decides to help. He uses his skills in dark magic knowledge to counteract the dark spells that have injured her. This could lead to a begrudging respect between them as they work together to heal her and keep the situation a secret from other Hogwarts students and staff.
The conflict could be Snape's pride. He is a proud man and asking for help, especially from a student like Hermione, goes against his nature. So he constantly battles his own ego while Hermione has to deal with his snarky remarks.
Hermione could start by showing her genuine intentions. For example, she could offer to help Snape with his potions research without asking for anything in return. Since Snape is passionate about potions, this might pique his interest and make him less resistant.
Snape would probably be quite surprised at first. Hermione is known for her academic prowess and self - sufficiency. His reaction could range from being dismissive, thinking she should be able to solve her own problems, to being intrigued by the nature of her request. If it's something related to the dark arts or a mystery in the wizarding world, his interest might be piqued, but he'd still be guarded in his response. He might even try to use her request as a way to gain some advantage or information for himself.
It could be that Bill is involved in some sort of mystery regarding ancient magic. Hermione, being a brilliant witch who loves to study and research, can assist him in deciphering the clues and understanding the complex nature of the ancient magic that he has stumbled upon.