Sentence b does not use an adverb clause
Odysseus tells Polyphemus that his name<span> was No Man, or </span>Nobody<span>, to trick the cyclops.
I'd say he did that so the cyclops will not be able to get help from his friends.
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The group that fought in the Trojan war was the Greeks.
To understand if they are noun phrases or not, it is necessary to understand its definition:
A noun phrase is a word or a set of words including a noun, whose function in a sentence can be: to act as a subject, an object or a prepositional object.
Sentence A is not a noun phrase. it is a prepositional phrase functioning as the postmodifier of the noun phrase (a lovely bouquet).
Sentence B is a noun phrase functioning as the subject of the sentence.
Sentence C is a noun phrase functioning as a direct object.
Sentence D is not a noun phrase, as it is a dependent clause and has not nouns in it.