In order for Marie to be willing to amend the friendship, her personality must be one that tends towards peace and compromise. The only word that means this out of the answers is "conciliatory."

Something you base your entire research on must be the most important part of it, and we should look for a word that conveys the importance of a hypothesis. "Paramount" fits here.

"Mawkish" means to be sickly sentimental. A poem without depth might very probably be dismissed as sickly sentimental or mawkish.

"Meager" means to be deficient in size or quantity. A salary deficient in quantity would understandably make it difficult to provide for a family.

"Officious" means to offer one's services when they are neither wanted nor needed.  Customarily, the best man arranges the bachelor party. Tony's meddling was cringeworthy, as it was unwelcome. 

"Pellucid" means easily intelligible and clear. Hemingway's prose is memorable for its intelligibility and clarity.

"Banal" means dull and commonplace. Because Jonathan paints unique and exciting works, it can be reasoned that he dislikes the dull and commonplace (that is, the banal).

"Incumbent," in this sense, means obligatory. A jury is obligated to be unprejudiced.

"Obstreperous" means noisy and unruly. Of course, noisy and unruly boys would be suspended.

Your clue to the word needed must be the list of words included in the sentence; there are five different art forms listed. Think about words that mean including several different but related things. Check to see if you know any parts of the answers included; do you recognize prefixes, roots or suffixes?

Part of the word “variegated” looks like variety or various so let’s keep that choice for now.

Parts of “incorruptible” seem familiar too; the prefix “in” usually changes the meaning of the root of the word to its opposite and “corrupt” means just plain bad. So incorruptible must mean something like not able to be made bad; that does not seem to relate to different art forms so let’s eliminate the choice. 

We have three more choices: eccentric, eclectic and thwarted. Try to remember if you have ever heard or seen these words in any context; in school, at home or on a television show? Sometimes the setting in which you saw or heard the words gives you a clue. Maybe you overheard someone saying that one of his teachers was very “eccentric”; do you know the teacher mentioned because that might give you a clue. The word “thwarted” is in the past tense. Why would a list of visual art forms be described using a verb in the past tense? I think we might eliminate the choice of “thwarted”.

Now we are left with “eccentric” and “eclectic”. The word eccentric includes “centr” which seems like a part of words like central or center or centrifugal; does this seem to describe art forms? NO.

Let’s choose the answer “eclectic” since there is nothing we can find to rule it out. Eclectic is the correct answer because it means having components from many different sources or styles. Always be brave enough to choose a word that you are unfamiliar wit if it is the only choice you cannot eliminate.