What Is the Best Time to Make Du’a on Friday?
Question

It is said that the du’a during the time of khutbah is accepted or there is a moment in that period when it is answered. It is also said while listening to the khutbah you should not talk and listen carefully. How can we make du’a when we are not allowed to talk or distract our concentration?
Praise be to Allah.Answering Du’a on Friday
The saheeh Sunnah indicates that there is a time on Friday when du’as may be answered. No Muslim happens to ask Allah for good at that time but He will give it to him. It says in the hadeeth narrated by al-Bukhari (5295) and Muslim (852) from Abu Hurayrah who said: Abu’l-Qasim (peace and blessings of Allah be upon him) said: “On Friday there is an hour when, if a Muslim happens to pray at that time and ask Allah for something good, He will give it to him.”  
Views on the time of answering du’a on Friday
There are many views on when this time is. The most correct are two views: 
Ibn al-Qayyim (may Allah have mercy on him) said: The most correct of these views are two which are mentioned in proven ahadeeth, and one of them is more likely than the other. 
The first is that it is from the time when the imam sits on the minbar until the end of the prayer. The evidence for this opinion is the report which was narrated by Muslim in his Saheeh (853) from Abu Burdah ibn Abi Moosa al-Ash’ari who said: ‘Abd-Allah ibn ‘Umar said to me: Did you hear your father narrating from the Messenger of Allah concerning the (special) hour on Friday? I said: Yes, I heard him say: I heard the Messenger of Allah say: “It is between the time when the imam sits down, until the prayer is over.” 
Al-Tirmidhi (490) and Ibn Majah (1138) narrated from Katheer ibn ‘Abd-Allah ibn ‘Amr ibn ‘Awf al-Muzani from his father from his grandfather that the Prophet (peace and blessings of Allah be upon him) said: “On Friday there is an hour of the day during which no person asks Allah for something but He will give it to him.” It was said, When is that time? He said, “When the iqamah for prayer is given, until the prayer ends.” [Shaykh al-Albani said: It is da’eef jiddan (very weak)]. 
The second view is that it is after ‘Asr, and this is the more correct of the two views. This is the view of ‘Abd-Allah ibn Salam, Abu Hurayrah, Imam Ahmad and others. 
The evidence for this view is the report narrated by Ahmad in his Musnad (7631) from Abu Sa’eed al-Khudri and Abu Hurayrah, that the Messenger of Allah (peace and blessings of Allah be upon him) said: “On Friday there is an hour when no Muslim happens to ask Allah for good at that time but He will give it to him, and it is after ‘Asr.” [In Tahqeeq al-Musnad it says: The hadeeth is saheeh because of corroborating evidence, but this isnad is da’eef (weak)]. 
Abu Dawood (1048) and al-Nasai (1389) narrated from Jabir ibn ‘Abd-Allah that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Friday is twelve hours in which there is no Muslim who asks Allaah for something but He will give it to him, so seek the last hour after ‘Asr.” [Classed as saheeh by al-Albani]. 
Sa’eed ibn Mansoor narrated in his Sunan from Abu Salamah ibn ‘Abd al-Rahman that some of the Companions of the Messenger of Allah (peace and blessings of Allah be upon him) gathered and spoke of the (special) hour on Friday, then they parted and did not disagree that it is the last hour on Friday. [al-Hafiz classed its isnaad as saheeh in al-Fath, 2/489]. 
In Sunan Ibn Majah (1139) it is narrated that ‘Abd-Allah ibn Salam said: I said, when the Messenger of Allah was sitting, We find in the Book of Allah that on Friday there is an hour when no believing slave happens to pray and ask Allah for anything at that time, but Allah will meet his need.
‘Abd-Allah said: The Messenger of Allah pointed to me, saying, “Or some part of an hour.” I said, You are right, or some part of an hour. I said, What time is that? He said, “It is the last hours of the day.” I said, It is not the time of the prayer? He said, “Indeed, when a believing slave prays and then sits with nothing but the prayer keeping him, he is still in a state of prayer.” Classed as saheeh by al-Albani. 
In Sunan Abi Dawood (1046), al-Tirmidhi (491) and al-Nasai (1430) it is narrated from Abu Salamah ibn ‘Abd al-Rahman that Abu Hurayrah said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “The best day on which the sun rises is Friday. On it Adam was created, on it he was sent down (to earth), on it his repentance was accepted, on it he died and on it the Hour will begin. There is no living being but it is in a state of apprehension on Friday from dawn until sunrise fearing the onset of the Hour, except jinn and mankind. On it there is an hour when no Muslim happens to pray and ask Allah for what he needs, but He will give it to him. Ka’b said: Is that one day in every year? I said: No, it is every week. He said: Ka’b read the Tawrat (Torah) and said: The Prophet (peace and blessings of Allah be upon him) spoke the truth. Abu Hurayrah said: Then I met ‘Abd-Allah ibn Salam and told him of my meeting with Ka’b, and ‘Abd-Allah ibn Salam said: I know which time it is. Abu Hurayrah said: I said to him: Tell me about it. ‘Abd-Allah ibn Salam said: It is the last hour of Friday. I said: How can it be the last hour of Friday when the Messenger of Allah (peace and blessings of Allah be upon him) said: “No Muslim happens to pray at that time,” but there is no prayer at that time. ‘Abd-Allah ibn Salam said: Didn’t the Messenger of Allah (peace and blessings of Allah be upon him) say: “Whoever sits waiting for the prayer is in a state of prayer until he prays”? I said: Then this is it.
Al-Tirmidhi said: A saheeh hasan hadeeth. Some of it is mentioned in al-Saheehayn. [It was classed as saheeh by al-Albani.] End quote from Zad al-Ma'ad (1/376). 
Should we make du’a during the Friday sermon?
According to the view that it is from the time when the imam sits down until the end of the prayer, that does not mean that the one who is praying behind the imam should distract himself with du’a and not listen to the khutbah, rather he should listen to the khutbah and say ameen to the du’a of the imam, and supplicate during his prayer, when prostrating and before the salam. 
By doing so, he will have offered du’a during this special time, and if he also says du’a in the last hour after ‘Asr, that is even better. 
And Allah knows best.