Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
If you cannot pray 20 lengthy Rakats, pray 20 brief Rakats. The important thing is: pray them. Do it out of love for Allah Ta'ala, and out of thanks for the gift of guidance and Sunnah of the Prophet (Sallallahu Alaihi Wasallam), which is the clear path to success in this life and the next.
Please refer to this link on 8 Rakat: http://qa.muftisays.com/index.php?viewpage=viewQA&question=2414
Also, refer to this link on 20 Rakat: http://www.muftisays.com/qa.php?viewpage=viewQA&question=2622
The 20 Rakat of Tarawih is the Sunnah of the Prophet (Sallallahu Alaihi Wasallam) and the consensus of the Sahabah (Companions) (Ijma-as-Sahaba). (al-Mughni vol.1, pg 803)
The four great Mujtahids, Abu Hanifah, Malik ibn Anas, Muhammad bin Idris Shafi'i al-Hashimi, and Ahmad ibn Hambal (Radhi Allahu Anhum) are in agreement that the Taraweeh consists of twenty Rak'ahs.
It was stated in Fayd ul-Bari Sharh Sahih al-Bukhari (by Shaykh Anwar Shah Kashmiri):
"Al-Imam Abu Yusuf (RA) asked Al-Imam Abu Hanifah (RA), 'Did Hadrat Umar (Radhi Allahu Anhu) have any compact from the Holy Nabi (Sall Allahu alaihi wa Aalihi wa Sallim) for 20 rak'ahs of Taraweeh?' The Imam replied, 'Hadrat Umar was not one to invent on his own; certainly he had some proof with him for this!'" (also found in Maraqi ul-Falah, pg. 81, by Imam al-Shurunbulali and Bahr ur Ra'iq, vol.2, pg. 66, by Imam ibn Nujaim al-Misri).
Imam Qurtubi states: “20 Rakat Tarawih and 3 Rakat Witr is the most authentic narration.”
Imam Nawawi (RH) states: “Tarawih is a unanimously accepted Sunnah (practice) of the Muslims, it is 20 Rakat.
Allamah ibne Taymiyyah (RH) writes, “this action (i.e. 20 Rakat Tarawih) of Umar (RA) is Sunnah and we have been ordered by the messenger (sallallahu Alaihi Wasallam) to hold fast to the Sunnah of the righteous Khulafa.
(Majmu' Fatawa Li Ibne Taymiyyah, Vol.22 Pg.234 and 276)
If one is absolutely unable to pray 20 Rakats, then one should do what one can, because, “That which one cannot do completely should not be left completely,” as the scholars explain. However, one should be remorseful, because one is leaving a confirmed Sunnah of Rasulullah (Sallallahu Alaihi Wasallam) and his Sahabah (RA).
And Only Allah Ta'ala Knows Best.