´It was narrated that Abu Hurairah said:` "The Messenger of Allah said: 'When you perform ablution, start on the right.'" (Da'if) Another chain with similar wording.
Hadith Referenceسنن ابن ماجه / كتاب الطهارة وسننها / 402
Hadith Gradingالألبانی:صحيح | زبیر علی زئی:ضعيف, إسناده ضعيف, سنن أبي داود (4141), انوار الصحيفه، صفحه نمبر 392
1؎ : From these hadiths it is understood that in ablution (wudu), one should wash the right hand first, and put on the shoe on the right foot first. Similarly, one should comb the right side of the head first, then the left side. This is the Sunnah, and this was the blessed habit of the Prophet (sallallahu alayhi wa sallam).
Narrated Abu Huraira (rad): Allah’s Messenger (rad) said: “When you perform ablution, begin with your right limbs”. [Reported by Al-Arba’a and garded Sahih by Ibn Khuzaima].
Shaykh Safi ur-Rahman Mubarakpuri
➊ Benefit: Although this narration is weak in its chain of transmission, its meaning is authentic, as established by other authentic narrations. It is proven that the Prophet sallallahu alayhi wa sallam preferred and loved to begin every good deed with the right side. He himself acted upon this and also commanded the ummah to begin from the right side.
Source: Bulugh al-Maram: Commentary by Safiur Rahman Mubarakpuri, Page: 42