Concept:
Indian philosophy is broadly divided into two categories:
• Astika (Orthodox) Schools -- Accept the authority of the Vedas.
• Nastika (Heterodox) Schools -- Do not accept the authority of the Vedas.
The six orthodox (Astika) schools are:
• Nyaya
• Vaisheshika
• Samkhya
• Yoga
• Mimamsa
• Vedanta
Step 1: Understand the meaning of Astika.
Astika schools believe in the authority of the Vedas and form the six classical schools of Indian philosophy.
Step 2: Identify the non-orthodox school.
Among the given options:
• Nyaya -- Orthodox (Astika).
• Vedanta -- Orthodox (Astika).
• Charvaka -- Heterodox (Nastika).
• Mimamsa -- Orthodox (Astika).
Thus,
\[
\boxed{\text{Charvaka}}
\]
is the school that is not an Astika school.
Step 3: Know about the Charvaka School.
The Charvaka philosophy:
• Rejects the authority of the Vedas.
• Accepts only direct perception as a valid source of knowledge.
• Emphasizes materialism and rational thinking.
Therefore, it is classified as a Nastika (heterodox) school.
Step 4: Final conclusion.
Hence, the school that is not an orthodox (Astika) school is:
\[
\boxed{\text{Charvaka}}
\]