Ruling on rinsing both the mouth and the nose with one handful of water
Question

Is rinsing both the mouth and the nose with one handful of water a Sunnah that is soundly narrated from the Prophet (blessings and peace of Allah be upon him)?
Praise be to Allah.Yes, the authentic and soundly narrated hadiths of the Prophet’s Sunnah which describe the Prophet’s wudu’ state that he used to rinse both his mouth and nose with one handful of water, and he would do that three times, using three handfuls.
Al-Bukhari (191) and Muslim (235) narrated that `Abdullah ibn Zayd (may Allah be pleased with him) said, describing the wudu’ of the Prophet (blessings and peace of Allah be upon him): Then he rinsed his mouth and nose from one handful of water, and he did that three times. Al-Bukhari included this hadith in a chapter entitled: Chapter: Rinsing the mouth and nose from one handful of water.
An-Nawawi (may Allah have mercy on him) said:
However the water reaches the mouth and nose, rinsing of the mouth and nose is achieved, but the best way is to rinse the mouth and nose with three handfuls of water, rinsing the mouth and then the nose from each handful.
This is mentioned in authentic hadiths in al-Bukhari and Muslim and elsewhere. As for the hadith which speaks of doing each action separately, it is weak; it is the hadith which says: I saw him rinsing his mouth and nose separately. Narrated by Abu Dawud, 139. Therefore the correct view is that one should do both actions with three handfuls of water, as we have mentioned above, because of the hadith of `Abdullah ibn Zayd.
End quote from Sharh Muslim, 3/105-106.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
Rinsing both the mouth and the nose with one handful of water is better than doing each action separately with a handful of water for each, because in the hadith of `Abdullah ibn Zayd, which describes the wudu’ of the Prophet (blessings and peace of Allah be upon him), it says that he rinsed his mouth and took water up into his nose then expelled it, three times, using three handfuls of water.
According to one version: he rinsed his mouth and nose with one handful of water, and he did that three times. Bukhari and Muslim.
According to another version: he rinsed his mouth and nose three times, from one handful of water. Narrated by al-Bukhari.
Something similar is narrated in the hadiths of Ibn `Abbas, `Uthman and others.
These hadiths are more numerous and more authentic than the hadiths which speak of doing the two actions separately. End quote.
Sharh al-‘Umdah, 1/177-178.
And Allah knows best.