"Labyrinthine" is an adjective that means either "like a labyrinth; irregular and twisting" when describing a network, or "intricate and confusing" when describing a system. So, we need to pick out an answer choice that means something like "irregular and twisting" or "intricate and confusing." "Simple," then, cannot be the correct answer, because "simple" is an antonym of "labyrinthine," not a synonym. "Convoluted," however, is an adjective that means "extremely complex and difficult to follow" and is often used of an argument, story, or sentence. Because "convoluted" is the answer choice closest in meaning to "labyrinthine," "convoluted" is the correct answer.

"Potent" means powerful or strong, so "powerful" is the synonym. 

"Futile" means useless, meaningless, not going to be successful. To further help you, "dreaded" means feared; "despair" is a feeling of sorrow and hopelessness.

The word "facile" means easy, or usually, too easy. To provide further help, "soporific" means sleep-inducing, causing exhaustion; "energizing" means gives energy; "malicious" means spiteful, intending to cause harm. To provide further assistance, "soporific" and "energizing" are antonyms of one another, just like "facile" and "challenging" are antonyms of one another. Synonyms are two words that have the same meaning and antonyms are two words that have different meanings.

“Anemic” means weak or feeble. The prefix a- means not or without, as evidenced in “anemic,” which means without strength, or “atheist,” which means without religion, without belief. To provide further help, “robust” means strong and reliable; “eloquent” means well-spoken; “erudite” means intelligent and well-read. 

"Ultimate" is an adjective meaning maximum, farthest, or greatest. So the answer choice closest in meaning is "utmost," an adjective meaning greatest, highest, or most. Considering the other answer choices, "worst" is the antonym of "ultimate" and an adjective meaning bad or faulty, "helpless" is an adjective meaning weak or dependent, and "trivial" is an adjective meaning of very little importance.

The word “facile” means very simple or easy. This is closest in meaning to “simplistic,” which means very simple. To provide further help, “abhorrent” means grotesque, horrific; “grotesque” means horrifying and repulsive; “banal” means boring or ordinary. 

The word "benign" means harmless. The best choice is "harmless" because it is a part of the definition of "benign."

"Ornate" is an adjective that means elaborate, so the answer choice closest in meaning to "ornate" is "decorated," an adjective meaning attractive or ornamental. Considering the other answer choices, none are close in meaning to "ornate": "plain" means clear; "empty" means vacant or not containing anything; and "full" means complete or containing as much as a container can.

"Intricate" means complicated or complex, so "complex" is the correct answer.