"Anarchy" means chaos, the lack of a political order. As a word it can be easily broken down to its component parts. The prefix an- means without and the root -arch- means leader, chief. So "anarchy" is without a leader, without a government, the lack of political order. 

The “-mersed” portion of this word is related to similar forms found in English words like “submerge” and “emerge.” It is derived from the Latin for to dip. The prefix “im-” is a version of “in.” Although “immersion” can describe the process of dunking someone into water, it likewise can mean that someone is completely absorbed in some activity. Consider a sentence like: “He was immersed in programming, little aware of anything in the world other than himself and his computer.” Likewise, we sometimes speak of people studying languages “by immersion,” that is, by living in the context of the language and using only the language being learned instead of their native languages for communication.

The word “vulnerable” comes from the Latin for wound. With the “-able” prefix, it would mean able to be wounded. Therefore, when someone is “in-vulnerable,” he or she is not able to be wounded. The word “invincible” does not necessarily pertain to wounds, but it does mean unable to be conquered. You may have heard of the famous line attributed to Julius Caesar: “Veni, vidi, vici,” “I came, I saw, I conquered.” The last word, “vici,” is a form of “vincere,” meaning, to conquer. To be “invincible,” is thus to be “un-conquerable.”

From the Latin "delectare," which means to delight (compare with the English cognate "delectable"), a "dilettante" is one who engages in an activity for the sheer enjoyment of it—an amateur or dabbler. Be careful not to confuse this word with "dilatory" (causing delay) or "debutante" (a girl making her "debut" into society).

The word “diffidence” literally means “not having faith” in oneself. The “-fidence” portion of the word is related to other English words pertaining to faith, such as “fidelity” and “confidence.” When someone does not have faith or trust in himself or herself, that person is often bashful or shy due to that lack of confidence. A related word, “diffident” is the adjective form of the word.

In the word “accelerate,” the “celer” portion means quick, coming from the Latin "celeriter," meaning quickly. The word “celerity,” therefore means quickness. It would be used in sentence like, “I am often surprised by the celerity of the deadly tree squirrel, which can kill its prey more quickly than many other animals.”

The word “amble” comes from the Latin for “to walk,” which is found in English words like “ambulatory” and “ambulate.” It means “to walk in a relaxed manner.” Among the options, “saunter” best describes such walking. One might say, “She ambled about the county paths, not wishing to hurry past any of the beauties of the autumn scenery.”

When something “mollifies,” it makes something softer. An “emollient” is a substance (e.g. a cream) that helps to make the skin softer. Although the word “mollify” can be used in this general sense of “softening,” it is often used to describe the specific case of “softening” emotions, that is to make someone less anxious. For this reason, “placate” is the best option among those given.

The word “vociferous” is quite recognizably related to the words “voice,” “vocal,” and so forth. The “-fer” portion of the word is derived from the Latin for “to carry,” as is found in the words “transfer” (to carry across) and “aquifer” (something that carries water between two or more places). The word vociferous means “carrying voice” in the sense of being loud or outspoken. For example, one could say, “At the proposition that she should change her political affiliation, the young woman became particularly vociferous, arguing passionately for her beliefs.”

Someone who is "diligent" pays attention to the details of something. For instance, a diligent student is one who studies much and does his or her work in a thorough manner. The word comes from the Latin for to love or take delight in, which is found in the word “predilection,” meaning a preference for something. If someone is "diligent," that person probably has a love for the activity on which he or she is focusing. A "meticulous" person is very careful regarding details, so this is the best option for this word.