Praise be to Allah.
Yes, it is mustahabb to pray four rak’ahs before Zuhr prayer and four after it. Al-Nasaa’i (1817) and al-Tirmidhi (428) narrated from Umm Habeebah (may Allaah be pleased with her) that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever prays four (rak’ahs) before Zuhr and four after it, the Fire will not touch him.”
The version narrated by al-Tirmidhi says: “Whoever regularly performs four rak’ahs before Zuhr and four after it, Allaah will forbid him to the Fire.”
The hadeeth was classed as saheeh by al-Albaani in Saheeh al-Nasaa’i.
These rak’ahs are not something different than the regular Sunnah (Sunnah raatibah) of Zuhr prayer, rather they are the regular Sunnah.
But what is certain and should not be abandoned under any circumstances is praying four rak’ahs before Zuhr and two rak’ahs after it. As for doing four rak’ahs after it, if a person does that following this hadeeth, then he has done the Sunnah and Allaah will reward him, but if he limits it to two rak’ahs, that is sufficient.
The time for offering the Sunnah prayer before Zuhr is between the adhaan of Zuhr and the obligatory prayer.
The time for offering the Sunnah prayer after Zuhr is from after Zuhr prayer until the adhaan of ‘Asr.
And Allaah knows best.