can anyone help me with providing an expalnation for each correct answer?

Pronoun-antecedent agreement B
12a. When a driver wants to buy a new vehicle, he or she usually test drives them. 12b. When a driver wants to buy a new vehicle, he or she usually test drives it.
Pronoun-antecedent agreement B
13a. Most presenters spoke without looking at his or her notes.
13b. Most presenters spoke without looking at their notes.
Pronoun-antecedent agreement B
14a. You may rent a movie or a video game for just one night if they are new.
14b. You may rent a movie or a video game for just one night if it is new.
Pronoun-antecedent agreement with indefinite pronouns A
15a. Neither the mayor nor the council members have filed their reports.
15b. Neither the mayor nor the council members have filed his reports.
Pronoun-antecedent agreement with indefinite pronouns B
16a. Anyone who requests a copy of the game may have it for their video library.
16b. Anyone who requests a copy of the game may have it for his or her video library.

12... vehicle(singular) is the antecedent of the pronoun... "them" is plural; "it" is singular.

13. Again, "presenters" is plural.
"his or her" is singular; "their" is plural.

14. "or" means one or the other, not both; therefore the antecedent is singular. "they" is plural; "it" is singular.

15. If any part of the subject is plural, then the antecedent is considered plural... so the pronoun must then be plural.

16. "Anyone" is one not many...so it is singular. Therefore, you need a singular pronoun.

congress usally resists a president's attemp to encroach on what they consider their authority.

To determine the correct answers for the pronoun-antecedent agreement questions, you need to ensure that the pronouns (he or she, them, their, his or her) agree with their antecedents (the nouns they refer to) in terms of number and gender. Here's an explanation for each question:

12a. When a driver wants to buy a new vehicle, he or she usually test drives them.
Explanation: In this sentence, the antecedent is "a driver," which is singular. Therefore, the pronoun referring to the driver should also be singular. The correct answer is 12b because "it" is a singular pronoun that matches the singular antecedent "a driver."

13a. Most presenters spoke without looking at his or her notes.
13b. Most presenters spoke without looking at their notes.
Explanation: In this sentence, the antecedent is "presenters," which is plural. Therefore, the pronoun referring to the presenters should also be plural. The correct answer is 13b because "their" is a plural pronoun that matches the plural antecedent "presenters."

14a. You may rent a movie or a video game for just one night if they are new.
14b. You may rent a movie or a video game for just one night if it is new.
Explanation: In this sentence, the antecedent is "a movie or a video game," which is singular. Therefore, the pronoun referring to the movie or video game should also be singular. The correct answer is 14b because "it" is a singular pronoun that matches the singular antecedent "a movie or a video game."

15a. Neither the mayor nor the council members have filed their reports.
15b. Neither the mayor nor the council members have filed his reports.
Explanation: In this sentence, the antecedents are "the mayor" and "the council members," both of which are plural. Therefore, the pronoun referring to them should also be plural. The correct answer is 15a because "their" is a plural pronoun that matches the plural antecedents "the mayor" and "the council members."

16a. Anyone who requests a copy of the game may have it for their video library.
16b. Anyone who requests a copy of the game may have it for his or her video library.
Explanation: In this sentence, the antecedent is "anyone," which is singular. Therefore, the pronoun referring to anyone should also be singular. The correct answer is 16b because "his or her" is a singular pronoun structure that matches the singular antecedent "anyone."

Remember that the correct pronoun choice depends on whether the antecedent is singular or plural and whether it is referring to a male, female, or a general or unspecified individual.