✅Answer: First, be sure to read questions 207, 116, and 114, and then pay attention to the following narrations:

1 عَنْ حَمَّادِ بْنِ عِيسَى عَنْ مُعَاوِيَةَ بْنِ وَهْبٍ قَالَ سَمِعْتُ أَبَا عَبْدِ اللَّهِ يَقُولُ كَانَ أَبِي يَدْعُو بِالطَّهُورِ فِي السَّفَرِ وَ هُوَ فِي مَحْمِلِهِ فَيُؤْتَى بِالتَّوْرِ فِيهِ الْمَاءُ فَيَتَوَضَّأُ ثُمَّ يُصَلِّي الثَّمَانِيَ وَ الْوَتْرَ فِي مَحْمِلِهِ فَإِذَا نَزَلَ صَلَّى الرَّكْعَتَيْنِ وَ الصُّبْحَ

📚 Tahdheeb, Vol. 3, p. 232

Translation: Mu'awiyah ibn Wahb said: I heard Imam Sadiq, peace be upon him, saying: My father would ask for ablution water when he was traveling in a palanquin, and a container with water would be brought to him, and he would perform ablution and pray eight rak'ahs (of the night prayer) and the Witr prayer. Then, when they dismounted, they would perform the two rak'ahs of the morning optional prayer and the morning prayer.

2 عَنْ حَمَّادِ بْنِ عِيسَى قَالَ سَمِعْتُ أَبَا عَبْدِ اللَّهِ يَقُولُ خَرَجَ رَسُولُ اللَّهِ إِلَى تَبُوكَ- فَكَانَ يُصَلِّي عَلَى رَاحِلَتِهِ صَلَاةَ اللَّيْلِ حَيْثُ تَوَجَّهَتْ بِهِ وَ يُومِئُ إِيمَاءً.

📚 Qurb al-Isnad, p. 10

Translation: Hammad said: I heard Imam Sadiq, peace be upon him, saying: The Messenger of Allah, peace and blessings be upon him, went out to Tabuk and prayed the night prayer on his mount, facing whatever direction it went, and he would gesture (for ruku and sajda).

3 عَنْ حَمَّادِ بْنِ عُثْمَانَ عَنْ أَبِي الْحَسَنِ الْأَوَّلِ فِي الرَّجُلِ يُصَلِّي النَّافِلَةَ وَ هُوَ عَلَى دَابَّتِهِ فِي الْأَمْصَارِ قَالَ لَا بَأْسَ.

📚 Tahdheeb, Vol. 3, p. 229

Translation: Imam Kadhim, peace be upon him, was asked about a person who prays a supererogatory prayer in a city while on a mount, and he said: There is no problem with that.

✅Based on the above narrations and other narrations on this topic, as well as the narrations mentioned in questions 207, 116, and 114, performing an obligatory prayer under specific conditions on a mount and performing a supererogatory prayer while traveling or in a hurry in cities, etc., is done with the same number of rak'ahs. There are no narrations indicating that the number should be doubled. Therefore, if we perform a supererogatory prayer on a mount, we perform each two rak'ahs as two, and the number is not doubled.

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Please review questions 114, 116, 207, and 308.