In the incident of Hilal ibn Umayyah, he accuses his wife of adultery, but her punishment was only 80 lashes. Kindly explain.

If a person accuses another of zinah and cannot prove it according to the conditions set by the Shar’iah then the punishment is 80 lashes. This is regarded as qathf. [1] So let’s say for example, A says, “I saw B committing zinah.”; the judge will ask A to provide witnesses (4 witnesses) if he can’t then A is guilty of qathf (blasphemy) and the punishment is 80 lashes.

If A is married to B then he is not obliged to provide 4 witnesses. He (A) will swear 4 times by Allah that his wife did commit zinah and then after that will say if he is lying then Allah's curse be on him. If the wife confesses then she is guilty of zinah and the punishment is stoning. But if the wife denies then she will have to swear by Allah 4 times that she did not commit zinah and then swear that if she is lying then may Allah's anger be upon her. This is whole process is known as mula'anah and Hilal ibn Ummayah was the first to use this avenue. After this the husband will be separated from the wife forever and may never remarry no matter what.[2]

Only Allah knows best.

References:

[1] Sh S Fawzan, A Summary of Islamic Jurisprudence, 2/457 – 463

[2] Sh S Fawzan, A Summary of Islamic Jurisprudence, 2/463