The answer is B. "If you don't mind," asked the student, "could we meet briefly after class today?"
If I was speaking to you without using quotation marks, I would say this to you, and it would be grammatically correct: If you don't mind, could we meet briefly after class today?
If you decide to quote somebody and place the name tag (asked the student) in between the sentence, you are going to want to remember that both times you use punctuation will be a comma. The first comma will never change unless it is a special circumstance. If I said to you instead: I like dogs. It would look like this:
"I like dogs," ojmichael said.
You are always going to want to end those with a comma and not a period. Now, the times when you are allowed to use a period will be like this. If you want to quote somebody without identifying who said, such as if two characters are back-and-forth arguing without any need for identification, and you're just trying to set a scene? It's going to look like this:
"I hate you, Lance."
"Shut up, Keith."
You do not end those with a comma unless you are going to specify who said what. If you did specify, it would change to a comma and then look like this:
"I hate you, Lance," Keith said.
"Shut up, Keith," Lance replied.
Another special case would be if your character performed an action after they spoke, and you did not choose to specify who specifically said it or how they did. I will take "Shut up, Keith" to show you.
"Shut up, Keith." Lance tilted his head back out of annoyance.
If you chose to write something like that, you would not use a comma because you have chosen here not to specify anything with a dialogue tag.
Now, when you split a sentence in half, it would look like this:
"Keith," he said, "she doesn't like you."
The reason this looks the way it does is because if I spoke to you without quotation marks and said: Keith, she doesn't like you, would I capitalize the "she?" (and if you see here, I placed the question mark within the quotations, even though I was not quoting she with a question mark. This is just how you are supposed to place punctuation). Because you would not capitalize the she normally, you would not capitalize the she while splitting the sentence. That is why it will never be:
"Keith," he said, "She doesn't like you."
That is wrong, wrong, wrong. You also do not capitalize the dialogue tag UNLESS it is a proper noun like a person's name. If you would not capitalize the word 'he' in the middle of a sentence, you would not capitalize it in the middle of a quotation.
The reason, now, that your actual answer to the question you asked is like this:
"If you don't mind," asked the student, "could we meet briefly after class today?"
The reason there is a comma again after the dialogue tag is because you have just interrupted a sentence. You have made the conscious decision to break up the sentence into fragments of the original, and therefore, a comma signals a continuation. If you were not splitting the sentence and you said something like "I like dogs." but, then you also decided to add on, "Though, they're kind of messy." after performing an action, it would look like this: "I like dogs," she said, messing with her hair. "Though, they're kind of messy." You would end up placing a period after the action, signifying a more permanent pause. The unnamed she has decided to stop talking to mess with her hair. She then chose to continue on.
