A "compass" is used to find direction in the act of navigation (the plotting or directing of a course for a ship or vessel). While this may seem like a tool-user relationship, it is not. The compass is part of the whole subject of navigation. Likewise, the answer will be part of a gemstone.  As all the words in the analogy set have been nouns, the answer should also be a noun.

The correct choice is "facet" (noun), which is one side of a multi-sided thing. Think of it as one of the flat sides of a jewel.  Its root "face" literally means face, appearance, or side. This is similar to how sides of 3D geometric shapes are often called "faces."

"Bauble" (noun) is a trinket or piece of jewelry, which makes it more a synonym of a gemstone.

"Peridot" (noun) is a type of gemstone, olive-green colored.

"Scarce" (adj) means uncommon, special, or rare. This describes the gemstone, rather than relating a part of one.

"Entombed" (adj) means buried, generally with a body, like in a grave or tomb. It was a common practice to bury wealth and treasures with someone of importance, but again, the word does not relate an example of a part of a gem.

A "battalion" is a group of soldiers within a larger army, something like a "regiment" or a "corps." So, to solve this analogy you need to determine which of these is a group of individuals who are collectively a part of a "company." The correct answer is a "branch" which means a regional department of a large company.

An "epilogue" is a part of a book that appears at the end. The correct answer will demonstrate a relationship of part and whole. A "coda" is a musical segment that appears at the end of a song. 

A "bouquet" is a group of flowers, particularly flowers that are held together in a bunch for the purpose of being given to someone. So, to solve this analogy, you need to determine what an "archipelago" is a group of. The correct answer is "islands."

The "hull" is the name given to the main body of a "ship." So, to solve this analogy you need to determine which of these a "fuselage" is the main body of. The correct answer is that a "fuselage" is the name given to the main body of an "aircraft." 

A "city" is often comprised of "boroughs" (districts within a city). So, to solve this analogy you need to determine what it is that a "dossier" is comprised of. Well, a "dossier" is a collection of "documents" pertaining to a certain subject. 

Theft is a form of crime; similarly, procrastination (putting things off) is a form of laziness.

Kindness is an example of a virtue. A virtue is a morally positive attribute which is opposite in definition to a vice. To solve this analogy you must identify which of the answer choices is an example of a vice. The only morally negative attribute is “selfishness” so this is the correct answer. For clarification serendipity means the accidental discovery of something fortunate; verbosity describes long-winded speech or writing.

An "altercation" is a form of negative, or hostile, conversation, so to solve this analogy you have to determine which answer choice relates to "tirade" in the same manner. "Tirade" means long and angry speech, so the correct answer is “speech.”

Homicide is a type of crime defined as the act of killing somebody, so to solve this analogy you have to determine into which category a tome belongs. A tome is a particularly long and heavy book so the correct answer is “book.”