When should one make Du'a after prayer? Prophet said that Du'a after offering Fardh prayers is accepted but I have also read Hadeeth saying that he used to stand after offering Fardh so fast as if he was sitting on a hot stone? So in a prayer for example, in Thuhr should we make Du'a after offering 4 Fardh or after completing the Thuhr that is after offering the last 2 Sunnah of Thuhr.

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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The time of supplicating after the prayer for whoever wants to do so is after finishing the legislated mention of Allaah that is reported in the Sunnah and which is recited after concluding the prayer. For details, please refer to Fatwa: 81736. So when the praying person concludes his prayer [by saying As-Salaamu alaykum] and mentions the legislated mention of Allaah, then he can supplicate as he wants. Supplicating before reciting the legislated mention of Allaah is not among the guidance of the Prophet .

Imaam Ibn Al-Qayyim said: 'Supplicating immediately after concluding the prayer facing the Qiblah or facing the people led in prayer is not from the guidance of the Prophet at all, and this was not reported from him.' As regards what was mentioned about the Prophet's standing quickly after the prayer, Imaam Muslim reported that 'Aa'ishah narrated: "When the Prophet would conclude his prayer he would not remain in his position except for the extent of time to say "Allaahumma anta As-Salaam wa minka As-Salaam tabaarakta yaa thal-Jalaali wal-Ikraam" (O Allaah! You are As-Salaam (which implies The One Who is free from all defects and deficiencies) and from You is all peace, blessed are You, O Possessor of majesty and honour!)". What 'Aa'ishah meant by ("he would not remain in his position") is that he usually didn't remain sitting facing the Qiblah, but would turn around to face his companions . So she did not mean that he stood up and left his position, but rather that he changed the position of his sitting to face his companions .

It should be noted that the narration mentioning 'he stands up as if he was on a hot stone', refers to his sitting in the second Raka'h for the first Tashahhud and this is not in relation to concluding the prayer." [At-Tirmithi]

Finally, it should be noted that the supplication habitually made in congregation after concluding the prayer in many countries is an innovation that has no basis in the Islamic Law.  

Allaah knows best.