Step 1: Article 246 read with the Seventh Schedule splits law-making subjects into three buckets - Union, State, and Concurrent. The Concurrent List is the shared zone where Parliament and the State legislatures both have authority.
Step 2: A useful health-policy memory hook: the spread of communicable disease across State borders is a shared concern, so its control sits on the Concurrent List (Entry 29). That points straight to choice (b).
Step 3: Centrally controlled matters - quarantine at international borders, nationwide drug standardisation, and regulation of mines and oilfields - are all Union List entries, eliminating (a), (c), and (d).
\[\boxed{\text{Prevention of extension of communicable disease from one unit to another}}\]