"Careen" means to move quickly and uncontrolled in a particular direction, or hurtle through somewhere.

"Dwindle" means diminish gradually, so "diminish," which means decline or decrease, is the correct answer. None of the other answer choices are close in meaning to "dwindle" and "diminish": "foretell" means predict or prognosticate; "hang" means dangle or suspend; "rotate" means spin or revolve; and "tease" means goad or mock.

"Capsize" means to overturn or to sink, and usually refers to ships. So, "sink" is the correct answer. None of the other answer choices are close in meaning to "capsize": "fulfill" means to carry out or complete a task or an assignment; "debate" means to discuss or argue about an issue or topic; "signify" means to indicate; and "mature" means to grow up physically or mentally.

"Embellish" means to "decorate" or to add ornaments to something; one might embellish a story by adding details that are not true to an otherwise true account. "Terminate" means to end or to conclude. "Mimic" means to imitate or to copy. "Plagiarize" means to copy another person's work without crediting that person for it. "Define" means to state the definition or qualities of a person or thing.

"Snare" is a word that can be used as either a noun or a verb, but because all of the answer choices can be used as verbs, we will need to consider "snare" as a verb. When used as a verb, "snare" means to trap or to catch and usually refers to trapping an animal, so "trap" is the correct answer.  None of the other answer choices are close in meaning to "snare" or "trap": "prosper" means succeed or flourish. "Contaminate" means pollute; "falsify" means mislead or show that something is false; and "research" means to study or investigate.

"Engender" is a verb which means to call forth. This can be used in the sense of creation of ideas, or in the sense of creating children.  "Spawn" can also mean to call forth. Additionally, it is, specifically, the laying of eggs by fish, amphibians or mollusks. 

"Dangerous" is an adjective which means causing harm.

"Ingratiate" is a verb meaning to flatter someone to create good will.

"Female" may seem like a good answer because it is a gender. "Engender" does not mean male or female, however.

"Duplicate" means to copy. This seems like a possible answer because, in the strictest sense, duplicating is an act of creation, just like engendering; however, "engender" has the connotation of creating something original:  an original idea or a child.  "Duplicate" is literally a copy of something else.  "Spawn" is a better answer because it, like "engender," has the connotation of creating something original.