The correct option is D (b)
Let’s examine the sentence: “After opening the door we entered into the room next to the kitchen.” Here, ‘entered’ is acting as a transitive verb. A transitive verb requires an object to complete its sense. This object can be provided by a noun, pronoun or gerund. So, the verb ‘entered’ would be followed by the noun ‘the room.’ To correct the sentence, the preposition ‘into’ after ‘entered’ would be dropped. The correct form of the sentence would be, “After opening the door we entered the room next to the kitchen.” Hence, error is in part b of the sentence. So, Option B is the correct answer.