The word "illustrious" comes from the Latin root meaning clear or bright.  Having a "luster" is to have a glow or a shine, and an "illustration" is something that makes its topic clear by means of a kind of example. Someone who is selfish thinks of himself or herself. This is the meaning of "ego-centric," which literally means "I-centered." We are therefore looking for a synonym of "illustrious." Generally speaking, this word means well-known—as though a bright light is visible. Such a person or thing would also be "eminent."

The "topography" of an area pertains to the physical character of that area—its hills, valleys, rivers, and so forth. The word comes from Greek roots that generally mean "place" (topos) and "drawing" (graphia). A map records an area's topography. A timeline records the ordering of occurrences. While this could be historical in nature, it could even be a timeline of scientific facts. The best option is therefore "chronology," which indicates an ordered set of events based on when those events occurred. It comes from the Greek for "time," kronos.

A tassel is placed at the end of a cord, generally as an ornament. (It is the little “stringy tuft” at the end of such cords). A “valediction” is a statement of farewell. The “valedictorian” of a class is so named because he is the one who says “farewell” on behalf of the class. (Also, he speaks after the salutatorian, who is the one who greets the class. The word “salutatorian” comes from words in Latin used to greet someone). Thus, among the options provided, the only proper case is “conversation,” for a “valediction” comes at the end of a conversation as a tassel comes at the end of a cord.

A novice is a person who is inexperienced or new to a given field of study or work. Thus, such a person is at the beginning of his or her work in that area. A “terminal” is something that is at the end of a structure or process. A terminal does necessarily occur only at the “finish line” (so to speak), as both ends of a (e.g.) stick can be considered its “terminal points.” Still, just as a novice is metaphorically at the beginning of his or her work, so is a terminal point (physically or metaphorically) at an end of a process or physical being. Since no other option captures this sense of “location” (whether physically or metaphorically), “end” is the best option for this analogy.

A "septagon" has "seven" sides, just as a "nonagon" has "nine" sides.

The word “pulmonary” comes from the Latin word for the lungs. It is used to in English to describe physical conditions related to these organs, as when someone has pulmonary embolism, which is a type of blockage of blood to the lung. Just as “pulmonary” describes the lungs, “cardiac” describes conditions related to the heart.

"Primary" and "first" are synonyms, just as "tertiary" and "third" mean the same thing.

A "guitar" and a "lute" are both stringed instruments, just as a "clarinet" and an "oboe" are both woodwind instruments. 

A syllable is a component of a word, a single unit of sound. We say that words are comprised of a number of syllables; therefore, we could write a bridge sentence like, “Just as a syllable is part of a word, so is a buckle part of a X.” While a buckle could be said to latch, snap, fasten, or secure, it is a part of none of these words. It is a part of a belt, which is a whole thing that has a buckle on it; therefore, this is the best option among those provided.

The pane of a window is the glass portion that is placed in the window’s frame. It is not the whole window but merely part of it; therefore, you could write a bridge sentence like, “As a pane is part of a window, so a phase is part of a X.” A phase is a portion of some undertaking or procedure. For instance, a project could be said to be in “Phase 1,” “Phase 2,” “Phase 3,” etc, depending on how much of it has been completed thus far. A procedure is like a plan or outline for a project, and it can be broken up into phases.