The meaning of the word “understated” can be guessed relatively easily, and you need not be suspicious of your hunch in this regard. It means state in a diminished way, as though to say that we “play down” something that is perhaps more important than is conveyed by such understatement. This can be done in a tasteful way—“understated jewelry” can still be quite beautiful. It can also be meant in a manner that indicates that someone is judging a person or thing negatively, “He understated his abilities, for he really believed himself to be talentless.” In contrast with such diminishing, “amplified” is the best antonym, as it means increased. To help you remember the word, think of a stereo system’s amplifier, which increases the output sound.

The word “puerile” is derived from the Latin for “boy.” The English word means “childish,” so this analogy is one of synonymy. When someone acts in a facetious manner, that person treats a serious manner in a way that is inappropriately flippant or light-hearted. Although facetious talk might be humorous, amusing, or even disrespectful, the best description is “flippant,” which is the correct answer for this analogy. 

The first half of this analogy is comprised of two very common words. Merely note that they are basically synonyms, so it will be necessary to find a synonym for “remorseful” among the options provided. To feel remorse is to feel sorry for a wrong that one commits. Among the options provided, only “contrite” expresses this same kind of emotional reaction. “Contrition” is the state of such remorse.  While words like “penance” and “atonement” might seem proper, these do not describe the actual state of sorrow felt for the wrong actions.

The prefix "per-" comes from the Latin meaning thorough. We see this in words like "perfect" and "pervade." When something permeates something else (e.g. a smell in a room), it completely fills it. Thus, permeate is a kind of "complete filling." To be "satiated" is to be satisfied completely. This is a kind of "complete satisfaction."

The prefix "juxta-" comes from the Latin meaning close. When two things are juxtaposed, they are bordering on each other (like neighboring plots of land). Just as juxtaposition is a close placement with regard to location, so is being "instantaneous" a kind of being close with regard to time.

When someone is "vexed," he or she is annoyed. This is the opposite of being calm. Therefore, we are looking for a word that is an antonym for "after."  he prefix "ante-" comes from Latin and means before. It is found in words like "antechamber" and "antecede." Something that is "anterior" is before something else. This is the opposite of being "after."

Someone who is malicious is not benevolent. Being benevolent means being "good-willed"—quite the opposite of someone with a malicious will, a bad will! Therefore, we are looking for something that is the opposite of "extraneous." The prefix "extra-" means outside of. Extraneous details are unimportant and irrelevant—as when someone tells you all about the recent weather when you ask him or her to give you an outline of the a class you missed. Therefore, extraneous details are not relevant.

To "vanquish" someone is to completely defeat him or her. Therefore, we are looking for a word that intensifies the meaning of "finish," giving the sense of being wholly finished. The prefix "per-" is from a Latin root meaning throughout, though it often means "thoroughly" or "completely." When something is perfected, it is completely made—it is totally finished.

The word "bedeck" generally means decorate. However, the prefix "be-" can also function as an intensifier meaning thoroughly. To "bedeck" something is to decorate it thoroughly. To be "bedecked" is to be covered or decorated very completely. Just as something dazzling is very illuminated, so too is something bedecked "very decorated."

When something is "cloying," it is excessively sweet. Therefore, our analogy is one of intensification. As something cloying is excessively sweet, so too is something "stellar" very good—exceedingly good. It comes from the Latin word for "star," as though the goodness of the thing in question were "as high as the stars."