Explanation:

The following are the 6 major systems of Indian philosophy:

Nyaya-Sastra was founded by Gautama Rishi, Nyaya literally means Logic. It is applied as a logical method itself, not only to describe a system structured according to the rules of logic.

Vaisheshika  was founded by Kanada Rishi. The aim of this philosophy is like that of the Nyaya Shastra. Salvation from suffering comes through Liberation of rebirth, wishes and ignorance.

Sankhya was founded by Kapila Acharya. According to this system, Knowledge of the elements of the Universe is essential in order to overcome the suffering of our existence and the difference between two these elements: PURUSHA (or Soul), and PRAKRITI (or nature).

Yoga or Yoga Shastra was founded by Rishi Patanjali, According to his teaching, the detachment of the Soul from nature (which is necessary in order to allow freedom from suffering), is possible.

Mimamsa was founded by Rishi Jaimini, According to his philosophy, the only possibility to overcome suffering is to correctly practise the ceremonies as described in the VEDAS.  

Vedanta philosophical school was grounded by Ved-Vyas. According to it, there is only one possibility for humans to be liberated from the suffering of existence which, according to his teachings, is true knowledge about God, man, the Universe etc. as stated in the VEDAS and UPANISHADS.

Lokayata and Kapalika  donot form part of 6 system of Indian philosophy

Charvaka, originally known as Lokayata and Barhaspatya, is the ancient school of Indian materialism. Charvaka holds direct perception, empiricism, and conditional inference as proper sources of knowledge, embraces philosophical skepticism and rejects Vedas.

Charvaka, also called Lokayata (Sanskrit: “Worldly Ones”), a philosophical Indian school of materialists who rejected the notion of an afterworld, karma, liberation (moksha), the authority of the sacred scriptures, the Vedas, and the immortality of the self.