So, it can't be a prepositional phrase, right? Those are typically a lot shorter than this and they begin with a preposition. (Often, though not always, a short word like in, on, under, over, before, after . . . you can look them up.)
The other three choices are all clauses. You know what a clause is? A group of words that has a subject and a verb. There are three types listed here: independent (stands on its own), dependent, and subordinate.
"Subordinate" and "dependent" mean the same thing in this context. A dependent clause and a subordinate clause are the same type of clause: they cannot stand alone. There are lots of different kinds of subordinate clauses, but by definition none of them are grammatically independent.
How can you tell a subordinate or dependent clause? Usually by the word it starts with. Subordinating conjunctions (words like although, because, while) begin one type of subordinate clause. Relative pronouns (who/whom/whose, which, that) and relative adverbs (where, when, why) begin another type. There's another class that's not so simple, but what all of these clauses have in common is they cannot stand alone as one complete sentence.
In that statement you cite, there's a subject (the Caldecott Medal) and a verb (is awarded) — and, in fact, with that alone you have a simple sentence. Everything else there is just an add-on to that basic sentence.
So this is a complete sentence. In other words, an independent clause.
Dexter thinks the economic success will offer him security.
Explanation:
He wonders if she is aware of his engagement to Irene, and he is confused by her sudden desire to marry him. Judy insists that he could never love anyone in the way that he loved her and expresses a wish to repeat their past, though Dexter is skeptical.
Judy asks that he drive her home, then she begins to cry, wondering why her beauty has not brought her happiness.
She makes a final appeal to Dexter for marriage, which inspires a wave of feelings in him. He settles on accepting her as “his own, his beautiful, his pride.” He decides to take Judy back.
