Translation:Sorry, can I borrow the notes from you?
"向" can mean "from" per https://resources.allsetlearning.com/chinese/grammar/Expressing_%22towards%22_with_%22xiang%22#Used_as_.22from.22. So, the latter half of the reference sentence is literally "I can from you borrow notes?" and follows a 向 + target + verb pattern.
It is more likely to explain it like " I am here facing to you." It is like a action that is intend to something or someone. Not only a meaning of "from' but also "to". for example, 我冲向他。I rush to him. I borrowed a pen from him.我向他借了一支笔。 我从他那借来了一支笔。(I borrowed a pen from him(there). 那（这）。。verb来direct object means "did something and gained something from xxxxxx(there).
This one expresses more polite. It sounds like you wanna borrow something from the stranger. The way between friends should be 我可以借你筆記嗎
Though this sentence gramatically means 2 opposite questions. But only can I borrow your note is frequently used. If you don't want confuse yourself, put 的 then becomes 你的筆記 is more clear.
By the way, here 跟 can substitute 向, 我可以跟你借筆記嗎 is also polite speaking. 向 is too polite not used often nowadays.