The correct answer for identifying the phenolic group is Option B, the Phthalein dye test.

Option A: Tollen's test - This test is used to identify aldehydes. Aldehydes are oxidized to carboxylic acids by the Tollen's reagent (ammoniacal silver nitrate), and this reaction results in a characteristic silver mirror or a black precipitate of silver metal, which is not relevant to phenolic compounds.

Option B: Phthalein dye test - The phenolic group can be identified using the phthalein dye test. In this test, phenols react with phthalic anhydride in the presence of a dehydrating agent, typically concentrated sulfuric acid, to form phthalein dyes. A common example of a phthalein dye that can be formed in this manner is phenolphthalein, which is synthesized using phenol and phthalic anhydride. These dyes exhibit color changes in different pH environments, which is a characteristic helpful in identifying phenolic compounds.

Option C: Carbylamine test - The carbylamine test, also known as the isocyanide test, is specific to primary amines. In this reaction, primary amines are heated with chloroform and an alkali base, typically potassium hydroxide, to produce a foul-smelling isocyanide or carbylamine. Since phenolic compounds do not have an amine group, they will not give a positive carbylamine test.

Option D: Lucas test - The Lucas test is used to classify alcohols of low molecular weight based on their reactivity with Lucas reagent, a solution of zinc chloride in concentrated hydrochloric acid. The test differentiates between primary, secondary, and tertiary alcohols. Phenols, which have an -OH group bonded to an aromatic ring, do not react in the same way as aliphatic alcohols in the Lucas test, and therefore, this test is not used to identify phenolic groups.

Thus, the test that is specifically used to identify a phenolic group is the Phthalein dye test.