None of the options provided here are great antonyms, but we can definitely remove bad candidates and find an answer that is good enough for our purposes. The word "ponder" means to think about deeply. To "scrutinize" something is to pay attention to its details, and to "observe" and "consider" are both options that at least note consideration of an object. Of course, observation and consideration are rather uninvolved in contrast to pondering. In another question, they might be options for correct answers. However, we have the option "disregard." This is more opposed to pondering than "observe" and "consider." Since "remark" is really not useful at all for our purposes, the answer must be "disregard."

The word "illuminate" is most often associated with its literal, physical notion—the phenomenon of light that illuminates a given surface. However, there are no words here that are directly related to such physical light. The word "illuminate" can be used to describe intellectual endeavors, when one thing "sheds light" on another—that is, makes the other thing clearer. In contrast to such illumination, there is the phenomenon of an overly complicated argument. When someone complicates a matter, he or she makes it less clear.

A set of "recollections" is a group of memories that have been gathered together. (Yes, the word is a bit like saying "re+collecting" as in "collecting together again.") When we recollect something, we attempt to bring back and report such a memory. If we do not call back such a thought, we then would omit it from such recollection. "Reminisce" and even "commemorate" are both rather synonymous, while "disabuse" and "retain" are neither synonyms nor antonyms for our purposes. Therefore, "omit" is the best option among those provided for an antonym.

When someone recants something, he or she "gives back" something that he or she held to be true. Generally, it is a question of recanting an opinion or a statement. For instance, we might say, "Thomas refused to recant his belief in Aristotle's writings, for he believed the Greek thinker to have spoken the truth." Thomas refuses to say that he no longer believes in the truthfulness of Aristotle. In contrast to such recanting, one can "assume" something by taking it up. Often this has the sense of "assuming an identity" or "assuming an uncertain fact to be true." The general point is that "assuming" means to take up as opposed to "recanting" which means something like to let go or give up.

When someone is culpable, he or she is guilty of something. Evidence or arguments that are "exculpatory" are ones that help to show the innocence of a person. They take away the guilt—"ex" (away) + "cuplate" (guilt / fault). The options "pardon" and "absolve" are both relative synonyms for this. To "defame" someone is to ruin his or her reputation. If there were no other options, this might pass for a distant antonym option; however, the best antonym option is "incriminate," which literally means to make into a criminal, or, by a more standard definition, to make someone seem guilty.

"Obfuscate" is a verb which means to make unclear; to confuse or bewilder. "Simplify" is a verb which means to make clear. This is the exact opposite of "obfuscate."

"Enigma" is a noun meaning a mystery or a puzzle. You may use an "enigma" to "obfuscate" a situation, but they are not antonyms.

"Stubborn" and "headstrong" are both adjectives meaning willful or determined.

"Plaudit" is a noun meaning praise.

"Athletic," "frisky," and "limber" are synonyms of agile. "Agile" means to be quick and well coordinated in movement.

"Lethargic" means to be drowsy or slugglish.

"Inert," "lethargic," and "lackadaisical" are synonyms of indolent. "Indolent" means slow or lazy, while "energetic" means full of energy.

"Nimble," "agile," and "limber" are synonyms of lithe. "Lithe" means moving or bending with ease, while "clumsy" means awkward in movement or action.

Something that is erratic has no pattern and happens at unknown intervals. The word is related to the word “err” and “error,” as these words all come from a Latin base that means “to stray.” When we make an “error,” we “stray from the right path.” Something “erratic” strays from any pattern—which would be like a straight line. In contrast to something “erratic,” “steady” is an excellent antonym.