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.
As for why many only pray 8, this is part of the Salafi/modernist attack on the worship of Muslims.
Please refer to this link on 8 Rakat: http://qa.muftisays.com/index.php?viewpage=viewQA&question=2414
The early Muslims Predecessors used to warn, “This matter is your deen [religion or way of life], so be careful as to whom you take your deen from.”
At the same time, 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.
Moulana Qamruz Zaman