Step 1: Charvakdarshanam.
The materialistic Charvaka Philosophy is attributed to Brihaspati. Therefore, A corresponds to II.
Step 2: Bauddhadarshanam.
Gautam Buddha founded Buddhist Philosophy (Bauddha Darshan). Therefore, B corresponds to IV.
Step 3: Yogadarshanam.
The Yoga school is associated with Hiranyagarbha and later systematized by Patanjali. Therefore, C corresponds to I.
Step 4: Vedantadarshanam.
The Vedanta system is attributed to Badarayana, the author of the Brahmasutras. Therefore, D corresponds to III.
Step 5: Final Matching.
The correct matching is A - II, B - IV, C - I, D - III.