Step 1: Understanding the Concept of Creation.
Visistadvaita Vedanta, a school of philosophy developed by Ramanuja, posits that the ultimate reality, Brahman, is personal and manifests the world as an extension of itself. In this system, the world is real and not illusory, and creation is seen as a process where God manifests the manifold world from Himself.
Step 2: Analyzing the Options.
- 1. Carvaka: Carvaka is a materialist philosophy that denies the existence of God and posits that the world is based on physical elements.
- 2. Samkhya: Samkhya is a dualistic philosophy and does not believe in a creator God but in the interaction of two principles: Purusha (consciousness) and Prakriti (matter).
- 3. Visistadvaita: This is correct. In Visistadvaita, God (Brahman) is seen as both the material and efficient cause of creation.
- 4. Advaita: Advaita Vedanta, proposed by Adi Shankaracharya, teaches that the ultimate reality is non-dual (Brahman is everything), but it does not describe the world as being created out of God.
Step 3: Conclusion.
The correct answer is 3. Visistadvaita.
Final Answer:
\[
\boxed{\text{The correct answer is 3. Visistadvaita.}}
\]