Step 1: Understanding the Concept:
An allylic alcohol is one where the hydroxyl (-OH) group is attached to an sp{3} hybridized carbon atom which is directly adjacent to a carbon-carbon double bond.
Step 2: Key Formula or Approach:
Look for the pattern: \( C=C - C(OH) \).
Step 3: Detailed Explanation:
(A) Benzyl alcohol: -OH on a carbon attached to an aromatic ring (Benzylic).
(B) Here, the -OH is on a Carbon that is attached to two methyl groups and is also directly bonded to an sp{2} carbon of a double bond. This follows the allylic pattern.
(C) Vinyl alcohol: -OH is directly on the double bond.
(E) This is a homoallylic alcohol (one carbon further away).
Step 4: Final Answer:
Option B is the allylic alcohol.