All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is a Sunnah (a recommended act) to rinse the mouth and nose from the same handful of water and this should be done three times. It is confirmed that the method of performing ablution by the Prophet is as narrated by 'Uthmaan : "…Then he put his hands (in the container of water) and pulled out water and rinsed his mouth and sniffed up water into his nostrils from the same handful of water, and he did this three times." [Muslim and Abu Daawood] Al-Bukhari reported the narration with the following wording: "…Then he took a scoop of water and rinsed his mouth and sniffed up water into his nostrils." Moreover, Ibn Hibbaan reported the narration with the following wording: "Three times with three handfuls."
Imaam An-Nawawi stated in his commentary on the book of Imaam Muslim : 'There is a clear evidence in this narration about the correct method, and that the Sunnah in rinsing the mouth and sniffing up water into nostrils is that it should be done in three handfuls of water, rinsing the mouth and sniffing water into nostrils from each one of them.' This means that he takes a handful of water and rinses his mouth with some of this water and immediately sniffs water into his nostrils from the same handful of water in order to rinse it after rinsing his mouth.
Allaah Knows best.