Quotation marks within quotation marks is mechanically incorrect. When referring to the title of an article, it is correct to place the title within quotation marks; however, when those quotation marks are within quotations, one should replace the quotation marks with apostrophes. The correct answer uses single quotation marks, the rest of the sentence is correct as written.

This sentence contains an error in the placement of the apostrophe. The word "hills" is the plural form of the word and should not contain an apostrophe (which would make it possessive). Note that apostrophes are never used to pluralize a word. Omit any and all apostrophes; the correct choice is, "Though the hills seemed small, the journey."

This sentence misuses the apostrophe. The word "cars" is supposed to be plural; apostrophes are never used to pluralize a word. Furthermore, the word "race (after "cars") is necessary because this verb (the first "race" is an adjective, describing "cars") describes what the cars are doing around the track. Without this verb, the last part of the sentence makes little sense. The correct choice is, "the race cars race around the track."

When another person is being quoted word for word, quotation marks are necessary. Since what Rebecca was saying to Ryan was being quoted word for word, quotation marks were necessary around what she was saying. 

However, if the words that another person said are being relayed indirectly or paraphrased, quotes are not necessary. Rebecca was telling Ryan indirectly what her mom had said, given that she said "mom told me that" (implying paraphrasing), rather than "mom told me" (implying direct quotation). 

Therefore, the correct version of the underlined portion of the sentence is "mom told me that we can't afford the farm anymore and"

In American English, single quotation marks ('') are used within double quotation marks (""), with punctuation appearing before any quotation marks.

The use of quotation marks in this sentence is incorrect, as a quotation within a quotation should always be set apart by single quotation marks inside the standard double quotation marks. The second mark must be changed to a single quotation mark and another single quotation mark should be inserted before the final double quotation mark. "Abraham Lincoln said, 'We must bind up the nation's wounds,'" the professor noted" is the only answer choice that correctly makes these changes.

Punctuation should always go on the inside of quotation marks. Compare the following two sentences:

"We have to leave".

"We have to leave."

The second sentence is correct. 

When a person's exact words are reproduced, quotation marks are required. When the quoted text contains a quotation, then single quotation marks are used to indicate that quotation. Also, when quoting, it is correct to include punctuation within the quotation marks. So, the correct version of the sentence is:

Thomas slumped in his chair, turned to me and said, "When I was young my grandfather told me that 'when the money's gone, it's time to go on.' I've listened to him so far, and I won't stop now."

In any piece of writing in quotation marks, even slogans or mottos, the punctuation that follows the final word must be placed inside the final quotation mark, excepting semicolons. Placing punctuation outside the quotation mark, as it is in this sentence, is incorrect. Only one answer choice, "the new charity campaign was “Making a Difference,” but the constant financial scandals," appropriately fixes the sentence.

When writing or reading dialogue, the spoken line should always end with a comma before the action words; furthermore, single quotes should only be used for quotes within other quotes. In normal cases, use double quotes.