Weather, as used here, means to endure or survive. A bad situation is something that you are likely to need to endure so to solve this analogy you have to identify which of the answer choices would be an appropriate response to a good situation. This should lead you to “revel” which means to enjoy the moment. For clarification, "provoke" means to illicit a reaction; "castigate" means to condemn; "implore" means urge; "degrade" means to make worse or dirty. 

Although "hammer" can mean several things, as it can be used as a noun or as a verb, in this case, we know that it is a noun because it is being compared to "tome," which means a scholarly book. A hammer is a tool used by a carpenter, so we need to pick out an answer choice that describes an occupation in which someone would use a tome. A tome is a tool used by a scholar, just as a hammer is a tool used by a carpenter, so "scholar" is the correct answer.

“Affix” is a verb that means fasten to something, while “post” is a word that can be used as a noun meaning a stable pole in the ground or a verb that means display a notice. So, the example either consists of a pair of synonyms, if “post” is being used as a verb, or a verb and a noun to which one might do that verb (one could affix something to a post). To pick between these interpretations, we will need to consider the potential answer choices. None of the potential answer choices fit the model of “a verb and a noun to which one might do that verb,” so we will need to consider the example to consist of a pair of synonyms, and pick out a pair of synonyms as the correct answer. While “explanation is to demand” and “verify is to substantiate” might each look like a potentially correct answer, “explanation” is not a verb, but a noun, so “explanation is to demand” cannot be the correct answer. “Verify,” however, is a verb that means make sure something is true, while “substantiate” is a verb that means provide evidence in favor of something, so the two words are synonyms, just as “affix” and “post” are synonyms, so “verify is to substantiate” is the correct answer.

“Tote” is a word that when used as a verb means carry something heavy, while “lug” is a verb that also means carry something heavy; so, that means that “tote” and “lug” are synonyms, and that we need to pick out an answer choice which also consists of a pair of synonyms. While “despondency is to determination” and “nag is to pester” might each look like a potentially correct answer, “despondency” is a noun that means a lack of optimism and courage, while “determination” is a noun that means resoluteness, so the two words are antonyms and “despondency is to determination” cannot be the correct answer. (Also, the two words are nouns, while the example consists of two verbs.) “Nag,” however, when used as a verb, means annoy someone by constantly asking about something, while “pester” means annoy someone by interrupting them often. So, “nag” is a synonym of “pester” just as “tote” is a synonym of “lug,” making “nag is to pester” the correct answer.