Can you please explain the following Hadith? Can you tell me what was the answer of this question?

A man said: “O Allah’s Apostle! If a man finds another man with his wife, [committing adultery], should the husband kill him?” Later on, I saw them [the man and his wife] doing li‘an in the mosque. (Bukhari)

The answer of the Prophet (sws) is not mentioned because the later part of the Hadith gives a good indication what his answer might have been. If a husband suspects his wife of having illicit relations with someone else, the process of li‘an has been recommended. The following is what the Qur’an says about it:

Those men who accuse their own wives [of adultery] but have no witness except themselves, each one of them shall be made to swear four times by Allah that his charge is true, and the fifth time calling down upon himself the curse of Allah if he is lying. As for the wife, the punishment shall be averted from her if she swears four times by Allah that his [her husband’s] charge is false and the fifth time calls down the wrath of Allah on herself if his charge is true. (24:6-9)

There is no way a husband can kill his wife or the man he sees her with for that reason. There are only two reasons for which a person can be killed and in both cases no individual can do it on his own. It has to be done by the state. The reasons are stated in the following verse:

Whoever kills a person, except as a punishment for murder or mischief in the land, it will be [written in his book of deeds] as if he had killed all the human beings on the surface of the earth. (5:32)

Courtesy: http://www.islamicissues.info/qa_question.php?qid=235