Answer:
The best answer is indeed letter B) Barking is a verb form being used as an adjective to modify the dog.
Step-by-step explanation:
In the sentence "The barking dog woke the entire neighborhood with his incessant noise," we have a verb form modifying the noun dog. "Barking" is the present participle of the verb "bark". The present participle is a verb form resulting from adding -ing to a verb root. Notice that it is not an adjective form, but it does function as an adjective in this sentence, since it is modifying a noun by attributing a quality to it.