Although "regards" has several meanings, one of them is almost interchangeable with "esteem," which means judgement or opinion.

Note that "estimation," a similar-sounding word, is completely unrelated.

Abroad most closely means overseas.  If someone travels or studies abroad, it means they go overseas to another country.

If someone has a hunch, it means they have an idea or feeling about a situation or something in particular.

"Rot" is a verb that means "decay or cause to decay by the action of bacteria and fungi; decompose." While something that is rotting might gross someone out, "gross out" does not mean the same thing as "rot," so it cannot be the correct answer. Because "decay" is the closest synonym to "rot" amongst the listed answer choices, "decay" is the correct answer.

"Wince" is a word that when used as a verb, means "give a slight involuntary grimace or withdrawing movement of the body in anticipation of pain or distress." "Flinch," a word that when used as a verb means "make a quick, nervous movement of the face or body as an instinctive reaction to surprise, fear or pain," is the answer choice closest in meaning to "wince," so "flinch" is the correct answer.

"Hoax" is a word that when used as a noun means "a humorous or malicious deception," and as a verb, "deceive with a hoax." So, "truth" cannot be the correct answer because "truth" is an antonym of "hoax." "Ruse," however, is a noun that means "an action intended to deceive someone; a trick." Because "ruse" is the answer choice closest in meaning to "hoax," "ruse" is the correct answer.

"Luster," when used as a noun, means "a gentle sheen or soft glow, especially that of a partly reflective surface," so we need to pick out an answer choice that is a noun and means something like "a gentle sheen." "Dullness" cannot be the correct answer, then, because "dullness" is an antonym of "sheen." "Shine," however, when used as a noun, means "a quality of brightness, especially from reflected light," and because "shine" is the answer choice closest in meaning to "luster," "shine" is the correct answer.

"Grasp" is a word that when used as a verb, means either "seize and hold firmly," "get mental hold of; comprehend fully," or "act decisively to the advantage of." As a noun, "grasp" means either "a firm hold or grip," "a person's power or capacity to attain something," "a person's understanding." So, we need to pick out an answer choice that is either a verb meaning "hold firmly," "comprehend fully," or "act decisively," or a noun that means "a firm hold" or "a person's understanding." So, neither "loose" nor "toss" can be the correct answer, because each of those answer choices is an antonym of "hold firmly." "Grip," however, when used as a verb, means "take and keep a firm hold of; grasp tightly," and because "grip" is the answer choice closest in meaning to "grasp," "grip" is the correct answer.

All of the answer choices can be used as verbs, so we need to consider "gorge" as a verb. When used as a verb, "gorge" means "eat a large amount greedily; fill oneself with food," so we need to pick out an answer choice that means something like "eat a lot." "Starve," then, cannot be the correct answer, because "starve" means "of a person or animal: suffer severely or die from hunger," making it an antonym, not a synonym, of "gorge." "Devour," a verb that means "eat (food or prey) hungrily or quickly," is the answer choice closest in meaning to "gorge," so "devour" is the correct answer.

"Pledge" is a word that can be used as a noun or a verb, but because all of the answer choices can be used as nouns, we will need to consider "pledge" as a noun. As a noun, "pledge" means "a solemn promise or undertaking," so we will need to pick out an answer choice that means something like "a solemn promise." "Treason," then, cannot be the correct answer, because "treason" means either "the crime of betraying one's country, especially by attempting to kill the sovereign or overthrow the government" or "the action of betraying someone or something," both meanings of which are far from meaning "a solemn promise." "Assurance," however, is a noun that means " a positive declaration intended to give confidence; a promise," and because "assurance" is the answer choice closest in meaning to "pledge," "assurance" is the correct answer.