Answer:
3. The purple elephant, a favorite toy, was lost somewhere underneath the bed.
Step-by-step explanation:
You want to identify the sentence in which the appositive is used correctly.
Appositive
An appositive is a noun phrase that follows a noun phrase and gives some explanation or some additional information. The preceding noun phrase is called the antecedent.
If the appositive is necessary to understanding the meaning, no punctuation is necessary. If it is merely useful information, it is set off by commas.
Application
Here the two noun phrases that are appositive phrases are "the purple elephant" and "a favorite toy." We judge one to be merely useful information relative to the other, so the second of these noun phrases should be set off by commas.
You only see that in sentence 3:
The purple elephant, a favorite toy, was lost somewhere underneath the bed.