Are the Eid prayer takbeers 6 or 12, and what is the legitimate opinion on how to reach a middle ground between the Hanafis and Salafis regarding this matter?

This is a matter of ijtihad (independent reasoning) about which the Companions, the Tabi'un, and the Imams held more than ten different opinions. The soundest tradition in the Sunnah is the hadith of Aisha, may Allah be pleased with her, that the Prophet, peace and blessings be upon him, would say seven takbirs in the first rak'ah and five in the second. This is the view of the majority of scholars.

This difference of opinion is permissible, and no one should be condemned for holding a differing view. Imam Ahmad held that all that has been reported from the Companions regarding the additional takbirs is permissible, and he believed that the matter is broad as long as there is no decisive text.

What is obligatory is to strive for the unity and gathering of hearts. It is not permissible to destroy this principle because of a recommended Sunnah. Calm discussion is commendable, but if no agreement is reached, then it is obligatory for Muslims to gather behind one Imam, and the worshiper must follow their Imam as long as the matter is one of ijtihad.