Step 1: Plan an elimination route.
Think of the school by its home: the Faculty of Fine Arts at Baroda. Ask which of these artists is better known for another centre. That artist is the odd one out, and it shows which options are wrong.
Step 2: Spot the odd one out.
Benode Behari Mukherjee is a Santiniketan master, a student and teacher of Kala Bhavana, and a muralist. He is the best-known name of the Bengal tradition in this list, not of Baroda. So A should not be selected.
Step 3: Remove options with A.
Option 1 (A, B, C) and option 3 (A, B, D) both contain A, so both are out. Options 2 and 4 are still alive.
Step 4: Decide between options 2 and 4.
The difference is the name D, Bhupen Khakar. He painted common people and small-town life in a story-telling manner, and he was a member of the Baroda circle of artists and critics. So D belongs in the list, and option 2 (which leaves D out) is incomplete.
Step 5: Why the other options fail.
Option 1 (A, B, C) wrongly keeps A, the Santiniketan artist, and drops D. Option 2 (B, C) is correct as far as it goes, but it is incomplete because D is missing. Option 3 (A, B, D) wrongly keeps A and drops C, so it makes two mistakes at once.
Step 6: Test the result with a second clue.
The Baroda School is known for story-like, figurative painting that mixed Indian life with ideas from world art. Subramanyan, Sheikh and Khakar all fit that description, each in a different way: Subramanyan through his teaching and murals, Sheikh through his narrative paintings, and Khakar through his scenes of ordinary people. Mukherjee's work, in contrast, is tied to the Oriental style of Santiniketan. This second clue points to the same answer as the first.
Step 7: Confirm B and C.
K. G. Subramanyan taught at Baroda for decades. Gulam Mohammed Sheikh studied and taught there too. Both belong, which agrees with option 4.
Final Answer:
Only option 4 (B, C and D only) lists exactly the Baroda artists.
\[ \boxed{4} \]