Step 1: Charvakdarshanam.
The Charvaka Philosophy, known for its materialistic outlook, is attributed to Brihaspatih. Hence, A → II.
Step 2: Bauddhadarshanam.
The Buddhist Philosophy (Bauddha Darshan) was founded by Gautam Buddhah. Hence, B → IV.
Step 3: Yogadarshanam.
The Yoga school is connected to Hiranyagarbhah, and later systematized by Patanjali. Hence, C → I.
Step 4: Vedantadarshanam.
The Vedanta system is attributed to Badarayanah, the author of Brahmasutras. Hence, D → III.
Step 5: Final Matching.
Thus, the correct match is A - II, B - IV, C - I, D - III.