When someone libels another person, he or she tells an untruth regarding that person (generally intending to ruin that other person’s reputation). The analogy could be written, “As a libel expresses an untruth, so a report expresses X.” The only answer that makes sense for “report” in this case is “data,” for this would be an object like “untruth” is with regard to libel.

A lunatic is someone crazy, and such a person’s actions could be called “lunacy.” The word means “the state of being crazy.” Surprisingly, perhaps, the word comes from the same base as does the word “lunar,” namely from the Latin for “moon.” It was believed that the personalities / attitudes of lunatics varied with the moon. Hence, they were given this name. The analogy could be rewritten, “As lunacy is generally insane behavior, so is maturity a state of X behavior.”  Someone who is mature sees the world in a level-headed and generally wise manner. Such a person could be called “sensible,” that is “wise or prudent.”

"Stubborn" and "obstinate" are strong synonyms; therefore a synonym for "callous" is "uncaring."

A “segue” is an immediate transition from one scene or song in a movie, musical, play, symphony, etc. It ultimately comes from the Latin for “to follow,” which we use in the phrase “non sequitur,” which means, “That does not follow from what went before it.” The analogy could be written, “As a segue is characterized by being immediate, so is eloquence characterized by X.” Eloquence is a persuasive form of speaking or writing. Often, the word is also used to describe a beautiful use of language. For our analogy, “convincing” best describes a characteristic of eloquence.

The word “subsidiary” is literally derived from the prefix “sub-” meaning “below” and the base meaning “to sit.” The base is related to words like “sedentary” and “sediment.” A subsidiary company is one that is run by an over-arching parent company. More generally, the term can be used to describe something that is of lesser importance in comparison with something that is overarching and more important. This subsidiary thing generally supplements the larger enterprise, offering aid. Thus, the analogy could be written, “As something subsidiary offers aid, so does something hindering offer (etc) X.” Note that we need to have some flexibility regarding the verb in the second half of the analogy. The best verb will be “create” or “make,” but that cannot be known until you start attempting to provide answers. Among the options, only “obstacle” describes that which something hindering creates. To “hinder” is to make something difficult for someone else.

A quagmire is literally a type of swampy area, though the term is often used metaphorically. In the latter usage, the term means “a complex and awkward situation.” (This would be like getting stuck in a bog, which would be a muck-covered, messy affair.) Something that is a quagmire could fairly be described as being confusing. We could potentially rewrite the analogy as stating, “As a quagmire can be characterized as being confusing, so can geniality be characterized as being X.” Something genial is friendly or cheerful. Such a thing would characteristically be enjoyable as well. This is the best option among those provided, since we are not looking for a direct synonym but an acceptable secondary characteristic.

A heap is merely a jumbled and disorganized pile of items. It has no unity or order. Thus, our analogy could be written, “As a heap is characterized by being jumbled, so is a system characterized by being X.” Generally speaking, a system is an interconnected whole, organized and ordered in a careful manner according to rules or laws. Such a thing is fairly characterized as being organized, which is the best answer among those provided.

"Fluid" and "liquid" are both synonyms, just as "warm" and "temperate" mean roughly the same thing.

"Cerebral" pertains to anything associated with the "brain," just as "oral" has to do with the "mouth."

"Ice" is a "solid," just as "vapor" is a "gas."