What does it mean when we say (a hadeeth/report was) “narrated by the two Shaykhs”? Who are they?
What is meant by “the two Shaykhs” is al-Imam al-Bukhari and al-Imam Muslim (may Allah have mercy on them).
Al-Bukhari is Muhammad ibn Isma’eel al-Bukhari (d. 256 AH). He wrote a book, Saheeh al-Bukhari, in which he compiled a number of saheeh ahadeeth (authentic prophetic traditions) from our Prophet (peace and blessings of Allah be upon him).
Muslim is Muslim ibn al-Hajjaj al-Nisaboori (d. 261 AH). He is the author of Saheeh Muslim. These two books – Saheeh al-Bukaari and Saheeh Muslim – are the soundest books of ahadeeth from our Prophet (peace and blessings of Allah be upon him).
If it is said of a hadeeth (prophetic narration) that it was “narrated by the two Shaykhs”, what is meant is that it was narrated by al-Bukhari and Muslim in their Saheehs. The same applies if it says “agreed upon,” i.e., al-Bukhari and Muslim both agreed on its narration.
Al-Nawawi (may Allah have mercy on him) said in the introduction to Sharh Muslim (1/14): The scholars (may Allah have mercy on them) are agreed that the soundest of books after the Holy Quran are al-Saheehayn, i.e., the two Saheehs of al-Bukhari and Muslim, and the ummah (global Muslim community) accepted that from them. The book of al-Bukhari is the sounder and more useful of the two. End quote.
And Allah knows best.