The phrase "always careful with his words" is an interrupting phrase, one that adds information to the sentence, but remains apart from its structure. All interrupting phrases must be set apart from the rest of the sentence by commas. "The coach, always careful with his words, intentionally avoided" is the only answer choice to appropriately use commas around the interrupting phrase.

The words "a long time activist" are an interrupting phrase, that is a phrase which interrupts the sentence and is not necessary for proper sentence construction, but does provide information. Such phrases must be set off by commas on either end, so "leader, a long time activist, urged" is the best choice among the answers.

The phrase "annoyed with her class" is what is known as an interrupting phrase. An interrupting phrase provides information, but is not necessary to the construction of the sentence. All interrupting phrases need to be set apart by commas, making "The teacher, annoyed with her class, got emotional" is the correct answer.

The phrase "reached through faulty logic" is an interrupting phrase, or one that gives crucial information to the meaning of the sentence, but is not necessary to the sentence's construction. All interrupting phrases must be set apart from the rest of the sentence by commas, making "The conclusion, reached through faulty logic, proved" the correct answer choice.

The phrase "a former player for the team" is an interrupting phrase, a phrase that provides extra information, but is apart from the structure of the sentence. All interrupting phrases must be separated from the rest of the sentence by commas, making "The new manager, a former player for the team, commented" the correct answer choice.

The phrase "worn out from his travels" is an interrupting phrase, or a phrase that provides additional meaning to the sentence, but stands apart from its essential structure. To show this, all interrupting phrases must be set off by commas on each end. This makes "The executive, worn out from his travels, barely" the correct answer choice.

The phrase "a close confidante for years" is an interrupting phrase, or a phrase that gives additional information without being crucial to the structure of the sentence. All such phrases need to be separated by commas, making "The advisor, a close confidante for years, gave" the correct answer choice.

The phrase "all still in high school" is an interrupting phrase, one that provides extra information to the sentence but is not a part of the sentence's main structure. Because of this separation, all interrupting phrase should be surrounded by commas; therefore, the correct answer choice is "The debaters, all still in high school, showed a maturity beyond their years."

When additional elements are put after or before the subject (in this case, "unaware of their country's") it should be separated by commas. Also look for the answer where "country" is in its proper possessive state: "their country's tense foreign relationship."

The phrase "a long time civic activist" is an appositive, a noun that renames a previously introduced noun while providing more information about that previously introduced noun. Appositives that can be removed from a sentence without affecting the sentence's meaning must be set apart by commas. "The speaker, a long time civic activist, urged" is the only answer choice that actually does this.