That the Prophet ﷺ at the time of washing his deceased daughter had said to them, "Start from the right side beginning with those parts which are washed in ablution."  

قَالَ النَّبِيُّ ﷺ لَهُنَّ فِي غُسْلِ ابْنَتِهِ ابْدَأْنَ بِمَيَامِنِهَا وَمَوَاضِعِ الْوُضُوءِ مِنْهَا  

The Prophet ﷺ used to like to start from the right side on wearing shoes, combing his hair and cleaning or washing himself and on doing anything else.  

كَانَ النَّبِيُّ ﷺ يُعْجِبُهُ التَّيَمُّنُ فِي تَنَعُّلِهِ وَتَرَجُّلِهِ وَطُهُورِهِ وَفِي شَأْنِهِ كُلِّهِ