Hey there!
A run-on sentence is a sentence that contains multiple ideas that could be split into multiple sentences but continues on without the use of transitions or punctuation.
Notice in the last sentence I just typed that I used the word "but" to link two related ideas together. I could have split that sentence into two, but kept it a single sentence and used a transition since the idea would flow better that way. Run-on sentences don't use a transition and just keep rambling on until an eventual stop.
Let's take a look at your answer choices:
"The concert started and the music was incredible." Notice how the word "and" is used to link the ideas. This isn't a run-on sentence.
"Holidays always go by too quickly since I get those days off." Again, "since" is used to link the two ideas together. This isn't a run-on sentence, either.
"They danced for hours; they never felt remotely tired." This is an example of a sentence that links two ideas together using punctuation. You could replace the semicolon with a period and the sentence would retain its sense and meaning. Since this is the purpose of semicolons, this isn't a run-on sentence either.
"Tomas was frustrated during class he forgot his book report." There's a word missing between these two ideas. Some sort of punctuation (a semicolon) or a transition (something like "since" or "because" would be good) is needed for this to make sense.
Your answer will be D.
Hope this helped you out! :-)