The correct answer is, What are you going to do after the movie is over, Billy? 

Each of these sentences are addressing "Billy". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

What are you going to do after the movie is over, Billy? 

Billy, what are you going to do after the movie is over?

What are you going to do, Billy, when the movie is over? 

The correct answer is, John, don't forget to finish your homework after dinner. 

Each of these sentences are addressing "John". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

John, don't forget to finish your homework after dinner. 

Don't forget to finish your homework after dinner, John. 

Don't forget, John, to finish your homework after dinner. 

The correct answer is, If you ask me, Ashley, this is the best taco that I've ever had.

Each of these sentences are addressing "Ashley". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

If you ask me, Ashley, this is the best taco that I've ever had. 

If you ask me, Ashley, this is the best taco that I've ever had.

Ashley, this is the best taco that I have ever had! 

The correct answer is, What are you going to do after the school year is over, Adley? 

Each of these sentences are addressing "Adley". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

What are you going to do after the school year is over, Adley? 

Adley, what are you going to do after the school year is over?

What are you going to do, Adley, when the school year is over? 

The correct answer is: Happy birthday, Brian!

Each of these sentences are addressing "Brian". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

Brian, happy birthday!

Brian, will you go to the store on your way home?

Happy birthday, Brian!

The correct answer is, Avery, don't forget to finish your chores before lunch. 

Each of these sentences are addressing "Avery". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

Avery, don't forget to finish your chores before lunch. 

Don't forget to finish your chores before lunch, Avery. 

Don't forget Avery to finish your chores before lunch. 

The correct answer is, If you ask me, Jason, this is the best restaurant I've ever been to.

Each of these sentences are addressing "Jason". When you address someone in a sentence, their name has to be set off with a comma or commas. Outlined below are the corrections for the incorrect answers:

If you ask me, Jason, this is the best restaurant I've ever been to.

If you ask me, Jason this is the best restaurant I've ever been to.

Jason, this is the best restaurant I've ever been to.

The correct answer is, No, I would not like anymore vegetables with my dinner. 

When you are answering a question with the words "no" or "yes" in a sentence, the words need to be set off with a comma. 

The correct answer is, First, let's begin by discussing the Revolutionary War. 

Introductory words need to be set off with a comma. Outlined below are the correct answers for the incorrect options:

First, let's begin by discussing the Revolutionary War. 

Finally, we will learn about the Civil War. 

Finally, we have made it to the end of the school year. 

The correct answer is: It's your birthday, Eric, and I hope it's a happy one.

When you're addressing someone in a sentence, that person should be set off by one comma if it is the first or last word (e.g. "Eric, I hope you have a happy birthday.") or two commas if it's in the middle of a sentence.  Only two answer choices properly separate Eric, who is being addressed in this sentence, by the proper comma use.

The other choice that does that is "Your mother, and I wish you a happy birthday, Eric." But that choice commits a different comma error by placing an incorrect comma after "mother."  You would use a comma there if it were a list of three or more people (e.g. "Your mother, your sister, and I wish you a happy birthday") but with only two people in that list the comma is incorrectly added.