What do you call a group of words that begins with a preposition and ends with an object?

A prepositional phrase is a number of words making a group that starts with a preposition and in most of the cases ends with a pronoun, a noun or a nominal phrase (a phrase that can function as the subject or object of a verb), which is called the object of the preposition.

A preposition is a word that links a noun or a pronoun to another word in the sentence. Some examples are “about”, “above”, “next”, “on”, "by", "besides", "at", and so on. Hence this, a prepositional phrase begins with a preposition and is followed by other words that give more information, like:  “She´s working for the money”, “My brother came here by bus”, “The painting of the sunset is beautiful”

Also, prepositional phrases can modify any part of a sentence; that´s why you can find them anywhere in the sentence: at the beginning, in the middle or at the end of it.

In English, a prepositional phrase can work as an adjective in which case is called adjective prepositional phrase, or as an adverb, in which case is called adverbial prepositional phrase,

The adjective prepositional phrase is named this way because it works as an adjective, meaning that gives information and describes characteristics of something or someone. For example, "My dad is a man of great wisdom”. What is in bold is a group of words (a prepositional phrase) that could be replaced by an adjective. It would be the same as saying “my dad is very wise”

On the other hand, the adverbial prepositional phrase is named this way because it works as an adverb, meaning that gives information about the way, the place, the time, and so on, regarding something. For instance: “My grandmother lives next block”. What is in bold is a group of words (a prepositional phrase) that could be replaced by an adverb. It would be the same as saying: “My grandmother lives there”.  

To sum up, the structures that begin with a preposition followed by a pronoun, a noun or a nominal phrase are a group of words called prepositional phrases.

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the answer is a)   a sentence of death costs the state "almost three times as much as a sentence of life in prison" (delon 147)