* சங்கரரை ஷன்மத ஸ்தாபகர் என்கிறார்கள்

*ஷண்மதம் தவறாக எழதபட்டுவிட்டது க்ஷமிக்கவும்

விளம்பும் ஆறு சமய மும்அவை யாகியும் மற்றும்தன்பால், அளந்து காண்டற் கரிய னாகிய ஆதிப்பி ரானமரும், வளங்கொள் தண்பணை சூழ்ந்தழ காய திருக்குரு கூரதனை,
உளங்கொள் ஞானத்து வைம்மின்
உம்மை யுய்யக்கொண்டு போகுறிலே.
நம்மாழ்வார் திருவாய் மொழி 4 10 9 (3114)

Velukkudidasan swami, namaskaaram.

‘Aaru samayamum’ means ‘ the six schools of philosophy which reject vEdham (namely chArvAka, SAkhya (baudhdha), kshapaNaka (jaina), vaiSEshika, SAnkhya and pASupatha)’.

Please refer this link:

http://divyaprabandham.koyil.org/index.php/2017/05/thiruvaimozhi-4-10-9-vilambum/

Thanks for asking this question, swami. 

adiyen dasan.

அடியேன் நமஸ்காரம்
வெகு காலமாக ஆழ்வார் சொல்லும் ஆறுசமயம் வைணவம்,சைவம்,சாக்தம்,கௌமாரம்,காணாபத்யம் மற்றும் சௌரம் என்று அடியேன் தவறாக நினைத்தது இருந்தேன்
தெளிவுபடுத்தியமைக்கு நன்றி
வேளுக்குடி தாஸன்

Srimate Raamnujaye Namaha,

Swamy there are 6 aasthika and 6 naastika religions..

Page 140 in the pdf in the link below describes this..
There are few variations in this classification

https://www.sadagopan.org/pdfuploads/Ramanuja%20Nutrandhadhi.pdf

The six darsanams that NammAzhwAr refers to here have been counted in number of ways to add up to a total of Six: (1) The six religions listed by AchArya RaamAnujA are Bhouddham, ChArvAkam, NaiyAyka-VaisEshikams of GouthamA, Jainam, Saankhyam and Yogam. These six are also known as Saakhya, ulUkhya, AkshapAtha,KshapaNa, Kapila and Pathanjali darsanams based on the people, who developed them or wrote commentaries. (2) In another counting, these six are recognized as Saankhyam, Yogam, Bhouddham, VaisEshikam, Jainam and Paasupatham. (3) In yet another counting, these six are: ChArvAkam, Jainam and four types of Bhouddham (VaibhAshikam and SautrAntikam of HeenayAnam and yOgAchAram and nihilism of MahAyAnam sects). The various darsanams listed above fall into the categories of Naasthika and Aasthika darsanams. The Naasthika darsanams like ChArvAkam (materialistic
atheism), Buddhism and Jainism are systems of thought that do not accept the authority of the VedAs and deny the tattvams such as Soul (Jevan) and God (Isvaran), which Aasthika mathams accept as fundamental to their beliefs. Naasthika mathams are called Veda Baahya mathams and the Aasthika Mathams are saluted as Vaidhika Mathams. The six Aasthika mathams are: NyAya, VaisEshika, Saankhya, Yoga, MimAmsa and VEDHAANTHA darsanams. Around 1000 CE, the NyAyA and vaisEshikA systems came together and became amalgamated into one system. There is not much of a difference between them now. Even among the set of six Aasthika mathams, there are different degrees of acceptance of the VedAs. NyAya, VaisEshika, Saankhya and YogA have admitted the validity of the VedAs in a tangential way, while staking their claims to be aasthika mathams. The MimAmsA and the VedAnthA are the truly Aasthika mathams.

Adiyen