What case is the Pasuk referring to?
Rashi, Ramban #1 and Rashbam: It refers to a case where her husband (or father) heard her Neder and endorsed it, 1 and then, even on the same day, 2 he annulled it.
Ramban #2 and Seforno: It refers to where, after remaining silent on the day that his wife made the Neder, he annulled it the following day in front of her. 3
What are the connotations of "Acharei Sham'o"?
What are the implications of "ve'Nasa es Avonah"?
Rashi and Ramban #1: It implies that he stands in her place to be punished, 1 because he caused her to sin 2 (And if someone who causes his friend to sin is subbject to punishment, jow much more is someone who causes his friend to do a Mitzvah subjet to reward ? Sifri).
Ramban #2: It implies that she is absolved from all guilt, since she was unaware of the fact that he knew about her Neder on the previous day 3 .
Ibn Ezra: It implies that [he is punished for her sin] because she is under his jurisdiction. 4
Seforno: Just like anybody else who causes his friend to sin under similar circumstances.
Rashi: We learn from here that someone who causes someone else to sin in this way, is punished instead of him.
Ramban: But in the event that she did know, she is guilty and he is absolved from her sin, and is only taken to task for not stopping her from sinning.
Ramban: He must hold that he forces her to transgress, but that not correct.
Why does the Torah present this case specifically by a husband and not by a father?
Ramban: As a matter of fact, the same Din will apply to a father, and the reason that the Torah presents the case by a husband is because, whereas it sometimes happens that a husband hates his wife and causes her to sin, a father generally loves his daughter and will not do that to her.