I am aware that Moaneqah is a kind of greetings which is famous between Muslims and apparently has so Thawab, but I'd like to know what the circumstances of it are. (According to Quran or Hadith)
Mo’aneqeh is considered as hugging or embracing each other (and putting the hands on the neck of each other). In fact, it is a sort of embracement when two Muslims visit each other. In other word, Muaniqah (المعانقه) is a kind of greeting (physical greeting) that when you visit each other, shake hands and hugging each other.
( کلینی، محمد بن یعقوب، الکافی، ج 2، ص 184، تهران، دار الکتب الإسلامیة، چاپ چهارم، 1407ق.)
According to a narration in Sunan ibn Majah it is something the Sahaba asked our Messenger and he said "no" and told them "to shake hands" instead but this Hadith was qualified as da'if similar riwayat on the matter here (in Arabic).
One of those riwayat is from Imam at-Trimidhi and was qualified as hassan!
So shaking hands is as far as i can tell the best to do when greeting each other. Even if we find other forms of greeting in our cultures. But it's according to some fatwa as you can read not forbidden!