"Transpire" means to take place, to happen, to occur. To provide further help, "misplace" means lose; "eradicate" means get rid of, completely eliminate; "frighten" means scare; "acknowledge" means recognize, notice. 

"Materialize" means to happen, to transpire, to occur, to take place, to become real and take place. To provide further help, "partition" means divide; "cleave" means split in two, divide; "toss" means throw; "lend" means allow someone to borrow. 

To "cringe" means to recoil, to turn away from or back away from in fear or disgust or embarrassment. To provide further help, "migrate" means move from one place to another; "extradite" means deport, allow someone to be taken out of a country so that they can be tried for crimes committed in another country; "banish" means send someone away as punishment and not allow them to return; deplore" means hate, loathe. 

To "persevere" means to keep going in the fact of difficulty. As such it is closest in meaning to "continue." To provide further help, "postulate" means suggest a possible theory, estimate; "halt" means stop, pause; "hesitate" means to pause or delay before saying or doing something; "aggregate," when used as a verb, means to combine, to come together. 

Perhaps you have heard of soil erosion. This is the process of topsoil wearing away from various causes. Often, water is involved in this process, though not necessarily always. That does not really matter for this question, in any case. The general idea is that erosion pertains to the "breaking down" of something over a period of time. The only option that expresses this idea is "dissolve." This is a very distant synonym—but a synonym nonetheless. 

The definition of "detain" is to confine or to keep from proceeding. The other answer choices do not match this definition; "release" is an antonym of "detain," "detangle" means to remove tangles, "avoid" means to keep away from, and to "identify" is to recognize or associate. 

The word "rue" means feel sorrow. "Regret," which means feel sorrow over a loss or a poor decision, is the best choice. Considering the other choices, "smell" means detect the scent of, "gather" means collect, and "study" means gather information about.

"Relish," when used as a verb, means appreciate greatly, so the answer choice closest in meaning to "relish" is "enjoy," which is a verb meaning take pleasure in. Considering the other answer choices, "dislike" is a verb meaning not enjoy or not like, "burden," when used as a verb, means give someone a thing or a task that causes them undue stress and worry, and "hide" is a verb meaning go to a location in order not to be seen or noticed.

"Rue" is a difficult word to figure out if you aren't familiar with it, as it's too short to be able to lend much help with roots. You may have heard the expression "rue the day," which people who speak a very formal English use when making threats. To "rue" means to lament or regret something. Don't confuse with the unrelated word "roué," which means a sexually immoral man.

When used as a transitive verb, to "gall" means to annoy or to make someone angry. It can also be used as a noun, in which case it means boldness or audacity. So, "annoy" is the correct answer. To help you, "debilitating" means greatly weakening, "choleric" means bad-tempered, and to "placate" means to calm or to soothe.