B is a prepositional phrase as it contains a prepositon as the head (throughout) followed by an NP (nominal phrase) which functions as the object.
A, C and D are not phrases but sentences. Consequently, they are composed of two parts: a subject and a predicate. For example, in "but they never stopped", the personal pronoun "they" functions as the subject of the sentence, that is, it's what the sentence is about. The rest of the sentence is the predicate, it tells something about the subject.
A is grammatically incorrect as it stands for an incomplete sentence. It contains the subject (they) and a main verb functioning as the head of the verbal phrase but it does not have the subordinate clause which should followed after the verb for the sentence to be considered correct. On the contrary, D is gramatically correct for it is a complete sentence. However, it is not a prepositional phrase because it is not a phrase but a sentence. The pronoun "it" is the head of the phrase and it is not a preposition. The verbal phrase "was a happy time" stands for the predicate, making the sentence grammatically correct. Said VP (verbal phrase) takes a nominal phrase as the object ("a happy time").
To sum up, prepositional phrases are made up of a preposition functioning as the head and its object. It can also contain modifiers. They take a nominal phrase as the object. That is why B is the correct answer. "Throughout" is the head of the PP (prepositional phrase) taking the nominal phrase "his life" as the object.
I believe you need to use subordinate clauses in order to combine these two sentences. Here is my solution:
During the Renaissance, (which was) an era immediately following the Middle Ages, new continents were discovered.
This way, you are using all words mentioned in both sentences, and combining them into one complete sentence.
Answer:
When my mom was a teenager she took "Cueca" dance classes. Cueca is a very popular type of dance in Chile, the country where she is from. To dance Cueca there has to be a couple dancing together. She took classes in a building near her house and sometimes her class put up shows for the public. These shows could be anywhere: at the beach, at a stage, at the park, wherever!
