To answer this question correctly, you must understand the distinction between the homonyms "then" and "than." "Then" refers to an event that happens after something, as in the sentence, "He came home from work and then watched television." "Than" compares two words or phrases, as in the sentence, "I like chocolate chip cookies more than peanut butter cookies."  So, "than" is the correct word to use in this situation, and "then" should be changed to "than" to correct the sentence's error.

The sentence uses "there" incorrectly. This is an easy mistake to look over since "there," "their," and "they're" are all homonyms—words that sound the same but have different meanings. The speeches politicians make about the issue belong to the politicians, so the proper form is "their," the possessive pronoun.

The key here is to distinguish between the homonyms "your" and "you're." 

"Your" is a possessive pronoun identifying something that belongs to you. The first usage here is correct because "your mother" refers to the mother that belongs to you.

"You're" is a contraction that combines "you" and "are," and this would be the correct choice for the second usage, making the corrected sentence "Your mother's signature cookie recipe is incredibly delicious, and I'm incredibly jealous that you're lucky enough to enjoy those sweet treats whenever you want them!"

This is an incorrect form of the word "its." Here, the sentence uses the possessive pronoun form of "its," but there is nothing being possessed here. Instead, this sentence needs to use "it's," the contracted form of "it is," to be grammatically correct.  The corrected sentence reads, "Even though it's only February, I am already excited for summer break and warmer weather."

"Here" is an adverb that means in this current location, but the sentence is using it as if it were the verb "hear," which means recognize sounds from or listen to.

To catch this sentence's error, you must understand the distinction between the homonyms "then" and "than." "Then" refers to an event that happens after something, as in the sentence, "She went to the movies and then to the store." "Than" compares two words or phrases, as in the sentence, "Driving is much faster than walking." To correct the sentence's error, "then" should be changed to "than."

You must understand the distinction between common homonyms to pick out the error in this sentence, particularly between "its" and "it's," as well as between "whose" and "who's." "Its" is a possessive pronoun, identifying something that belongs to "it," so the phrase "I bet its owner is looking for it" is correct. You can eliminate that answer choice from your options. However, "who's" is a contraction of the words "who" and "is," which does not fit in this sentence ("I'm not sure who is jacket this is" wouldn't make sense) and is therefore an error. "Whose" is a possessive pronoun, signaling that the noun belongs to someone, so that would be the correct form here. ("I'm not sure whose jacket this is").

"Affect" and "effect" are two commonly confused homonyms. The best way to remember the difference between them is to remember that one is used most often as a noun and the other as a verb. "Affect" is a verb that means to influence something, while "effect" is a noun that means the result of something. ("Effect" can also be used as a verb that means to cause, as in the phrase "effect change.") One should use the word "effect," not the word "affect," in this sentence.

This sentence's error has to do with the homonyms "to," two," and "too." The "two" in "two large slices of chocolate cake" is correct; this form of the word refers to the whole number greater than one but less than three. The "to" in "to her friend's birthday party" is also correctly used; this "to" is being used as a preposition. The "to" in "to make odd gurgling noises" is also correctly used because it is part of an infinitive verb, "to make." The "to" in "eaten to much" is incorrect, however; to correct the sentence, one would need to change this "to" to "too," which is used to mean in excess or in an amount that is greater than what is needed or desired.

This sentence's error is its use of "than," a word that is used to form comparisons like "He is taller than her," where it needs to use "then," which is a word that designates a specified time in a sequence in the past, as in the sentence "I almost bought the giant purple trampoline for my apartment, but then I decided not to." To correct this sentence, "than" should be changed to "then."