1. The sentence that contains a misplaced modifier is D) Flying high above the clouds, Austin saw the airplane.  

Modifiers are words, phrases or clauses that provide a description of another word or group of words in a sentence. In this sentence, the participle clause Flying high above the clouds is modifying the noun airplane. However, the modifier is misplaced because it is too far from the noun it is modifying and therefore, the meaning of the sentence is confusing.

2. The sentence that contains a dangling modifier is B) While swimming, the towels did not have a chance to dry.

In this sentence, the participle clause While swimming is the modifier, however, it is not modifying the noun the towels, as it seems. In this case, the sentence should be paraphrased in the following way: The towels did not have a chance to dry while we were swimming.

3. The adjective phrase is B) most famous.

An adjective phrase is a phrase that contains an adjective governing the phrase. In this sentence, most famous is the superlative form of the adjective famous.  

4. The adjective phrase is B) is a popular area.

In this sentence, the adjective phrase is popular area since it contains as a main element the adjective popular, which is describing the noun phrase the sidewalk.

5. The adverb phrase is C) across the field.

An adverb phrase is one that functions as an adverb within the sentence. In this case, across the field is functioning as an adverb of place, describing where the signals were sent.

6. The adverb phrase “with a smile” is modifying A) Maria.

In this sentence, the adverb phrase functions as an adverb of manner, modifying the noun Maria. The adverb phrase is indicating how Maria watched her little girl sing.