Assalaamu alaykum Shaikh. While reading Sahih Al-Bukhaari, I read the following hadith that I already knew. Volume 1, Book 10, Number 560: Abu Sa'id Al-KhudriI narrated that he heard the Prophet, sallallaahu ‘alayhi wa sallam, say, "There is no prayer after the morning prayer till the sun rises, and there is no prayer after the ‘Asr prayer till the sun sets." However, I also found these hadiths that say that the Prophet prayed two rak'ahs after the ‘Asr prayer. Volume 1, Book 10, Number 564: ‘Aa’ishah narrated, "By Allah, Who took away the Prophet, the Prophet never missed them (two rak'ahs) after the ‘Asr prayer till he met Allaah, and he did not meet Allaah till it became heavy for him to pray standing, so he used to offer most of the prayers sitting. (She meant the two rak'ahs after the ‘Asr) He used to pray them in the house and never prayed them in the mosque lest it might be hard for his followers, and he loved what was easy for them. Volume 1, Book 10, Number 565: Hisham's father narrated that ‘Aa’ishah told him, "O son of my sister! The Prophet never missed two prostrations (i.e. rak'ah) after the ‘Asr prayer in my house." It confuses me. Is praying two rak'ahs after ‘Asr from the Sunnah or is it forbidden? And I coud not understand the following hadith either; could you please explain it? Volume 1, Book 10, Number 561: Mu’aawiyah said, "You offer a prayer that I did not see being offered by the Prophet, sallallaahu 'alayhi wa sallam, when we were in his company, and he certainly had forbidden it (i.e. two rak'ahs after the ‘Asr prayer).

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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger. 

The view held by the majority of the scholars is that it is forbidden to pray after ‘Asr. They argued that the prayer of the Prophet after ‘Asr was peculiar to him, as he once missed the Sunnah after the Thuhr and then prayed it after ‘Asr, and his habit was that if he began an act of worship, he would do it continuously; so he continued to observe these two rak'ahs after the ‘Asr prayer.

As-San'aani said in Subul as-Salaam:

“As for him praying two rak’ahs after the ‘Asr prayer in his house – as reported by Al-Bukhari and narrated by ‘Aa’ishah, 'He never abandoned two prostrations (rak'ahs) after ‘Asr in my home;' and another narration reads, 'He never abandoned them neither loudly nor secretly.” – then the answer given for this is that he prayed them as a way of making up for the two supererogatory rak’ahs after the Thuhr when he missed them, and then he continued to pray them because when he began an act of worship he would continue doing it, so this is evidence that it is permissible to make up for a missed prayer at a time when it is disliked to perform prayer. Also, it is peculiar to him that it was permissible for him to perform supererogatory prayers at that time, as evidenced by the hadeeth by ‘Aa’ishah, reported by Abu Daawood, which reads, “… he used to pray after the ‘Asr but forbade others from doing it, in the same manner that he fasted for three consecutive days [without breaking the fast on the first or second day] while he forbade others from doing it.”

As regards the hadeeth by Mu’aawiyah that you mentioned, then its meaning is clear; he forbade people to perform supererogatory prayers after the ‘Asr prayer, and he (Mu’aawiyah) mentioned that he did not see the Prophet pray after the ‘Asr; this is according to his knowledge because the Prophet used to perform the supererogatory prayer after the ‘Asr in his home, as reported by ‘Aa’ishah and others, and we have already answered about his prayer after the ‘Asr prayer as per the view of the majority of the scholars.

Allaah knows best.