All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Taraweeh prayer {Night prayer during Ramadan} is an act of Sunnah and there is a consensus amongst the schools of Ahlu Sunnah Wal Jama a that it is twenty Rakahs. Rather, the Maliki school is of the view that it is thirty six Rakahs. Based on this, one who performs eight Rakahs performs part of this Sunnah, and will be rewarded accordingly.
It goes without saying that Taraweeh prayer is the night prayer performed during Ramadan, and the Prophet (PBUH) said about it: "Whosoever performs (optional Tarawih) prayers at night during the month of Ramadan, with Faith and in the hope of receiving Allah's reward, will have his past sins forgiven."{Muslim}.The Imams of the Sunni schools of thought have reported the manner of its performance from the righteous predecessors {As-salaf As-Saleh} to the lifetime of the Noble Companions. As`sa`ib Ibn Yazeed said, "During the caliphate of Umar Bin al-Khattab, they used to perform twenty Rakahs of Taraweeh prayer and the reciter of the Qur'an would recite the Mi'in (a group of medium-sized suras) "{Related by al-Baihaqi}.
This is the practice in the two holy mosques in Mekha and Medina as well as other Islamic countries. Whoever can perform the twenty Rakahs will have performed the complete Sunnah, but whoever performs some will be rewarded accordingly.However, he has no right to ban or forbid anyone from completing the twenty Rakahs since forbiddance must be used against iniquities; whereas, prayer is amongst the best of righteous acts done by a believer. The Prophet (PBUH) said, "Prayer is the best act of worship, so pray as much as you can"{Related by Tabarani}. Allah, The Almighty, said, " Seest thou one who forbids-A votary when he (turns) to pray?" And Allah knows best.