What is the hadith regarding the number of rakat in Taraweeh prayer, and is it obligatory to pray the full amount?

So there are different views. Is it 8 rakah? Is it 20 rakah? Various different views. The key point in all of this though, and this really summarizes everything, the Prophet sallallahu alayhi wa sallam, what did he say? He said, مَن صَلَّى مَعَ الْإِمَامَ حَتِّين سَلِفْ كُتِبَ لَهُ قِيَامُ اللَّهِ The hadith collected inside Muslim. Whoever prays with the imam until the imam finishes, you will have the reward as if you prayed the entire night. So if your imam prays 8 rakah, you stay for the entire 8 rakah. If the imam prays 20 rakah, you stay for the entire 20 rakah. And then you go home, you could be having a cup of tea, do whatever it is that you want to do. You're still getting rewarded as if you prayed the entire night. Why? The key point being you finish when the imam finished. So try never to leave early. Always stay till the imam finishes and you have the rewards if you pray the entire night. And don't worry about the difference of opinion. Just focus on the hadith of the Prophet sallallahu alayhi wa sallam and the reward of getting for the entire night.