Rashi: It means with witnesses and warning.

Kidushin, 9b: It implies that he married (betrothed) her through Bi'ah (intimacy) - to teach us that a man can aquire a woman through Bi'ah. ¹

Sifri: To include where she was intimate whilst still in her father's house and was betrothed at the time when she sinned.

Rashi and Ramban (both citing the Sifri): It implies that both the adulterer and the adulteress must derive pleasure equally in order to be Chayav, to preclude where the man is 'intimate' with the woman on other parts of her body, where he derives pleasure but she does not ¹ - in which case they are both Patur.

Oznayim la'Torah: Because in Pasuk 20, in connection with where the husband's accusation is verified, it only mentions that the girl is stoned, but not the adultere - presumably because his identity is not known, or because he fled.

Rashi #1 (according to the text that reads 'me'Achareihem'): It comes to include where, after Reuven and Rachel have been sentenced to death, Reuven has relations with Leah, who is also married, or where Shimon has relations with Rachel, both the second woman and Shimon respectively, are Chayav. ¹

Rashi #2 (according to the text that reads 'me'Achoreihem', citing the Sifri): It comes to include where they are intimate she'Lo ke'Darkah (from the back). ²

Rashi #3 and Targum Yonasan: It is coming to include where the woman is pregnant - to teach us that they do not wait until the baby is born, but carry out the death-sentence immediately. ³

Ramban: The Torah writes "Gam Sheneihem" in connection with the woman, as if to say that she is also Chayav - because we may otherwise have thought that she is Patur, since it is the man who generally accosts the woman and seduces her, and who is active. ⁴

Ramban #1: The Torah is merely explaining "u'Meisu Gam Sheneihem", as it often tends to do. ¹

Ramban #2 (citing the Sifri): To teach us that the man is Chayav even if the girl (is not, because she) is a Ketanah, and the woman is Chayav even if the boy (is not, because he) is a Katan.

Targum Yonasan: They are subject to Chenek (strangulation). ¹

Oznayim (citing the Ri Avuhav): The reason that the Torah is lenient by a Na'arah Me'urasah in the field - even though the witnesses did not hear her scream - is because a Na'arah guards her Besulim, and even more so when she is betrothed - for fear that her Chasan will discover her infidelity, and that she will bring upon herself shame and disgrace if he does - as opposed to a married woman to whom this area of fear is not applicable.

Oznayim la'Torah (in Pasuk 24): Because, bearing in mind that her death shows up her poor upbringing at the hand of her parents, by a Na'arash Arusah it is necessary to execute her 'by the entrance of her father's house' - because people will otherwise assume that she committed adultery after having entered the house of her parents-in-law (after the marriage), whereas if the witnesses comne after she is married, everyone will know that it has nothing to do with her parents-in-law, and will place the blame on her parents even if she is killed at the entrance to the town ¹ (the ideal location) ² .