All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
‘Aa'ishah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, liked Tayammun (i.e. starting with the right side) when putting on his shoes, combing his hair, performing ablution and bathing, and in all his affairs. [Al-Bukhari and Muslim] This hadeeth indicates that it is recommended to start with the right side in these actions and their like. There is nothing narrated in the Sunnah, as far as we know, indicating that it is recommended to start with the right and then move completely to the left; rather, some scholars said that it is recommended to move gradually from the right to what follows on the left, and that doing this is part of Tayammun as well. Shaykh Ibn ‘Uthaymeen wrote about the manner of cutting the nails:
"Trimming the fingernails should be done in conformity with the hadeeth of ‘Aa'ishah, who said, 'The Prophet, sallallaahu ‘alayhi wa sallam, used to like Tayammun in wearing his shoes, combing his hair, performing ablution and bathing, and in all his affairs.' So the person starts with the fingers of the right hand: the right little finger, then the ring finger, then the middle finger, then the index finger, then the thumb; then the fingers of the left hand: the left thumb, then the index finger, then the middle finger, then the ring finger, then the little finger. It should be noted that this order may be difficult to follow."
Al-Haafith Ibn Hajar quoted the following from some scholars of Fiqh, "Tayammun in this regard is to start with the little finger of the right hand and end with the little finger of the left hand and to do the same with the toes..." [Fat-h Al-Baari]
He also said, "He starts with the small toe of the right foot to the big toe, then the big toe of the left foot to the small toe..."
We did not find a similar statement from the scholars regarding combing the hair; so the direction of combing the hair is flexible, Allah willing.
Allah knows best.