Take a look at the sentence again:
In preparation for the quiz, La'Mia studied comma splices and fused sentences
until she thought her brain would burst, finally,
she put away her notes, convinced that she would remember the rules even
on her death bed.
For a sentence to be fused, you must have two complete sentences run together with no punctuation. In the example above, a comma joins the two sentences. La'Mia studied comma splices and fused sentences ... begins one sentence. Finally, she put away her notes ... starts the second sentence. Thus, this error is a comma splice.
Remember that both comma splices and fused sentences are major errors. They make your reader think that you cannot write a correct sentence. Because the sentence is the most basic building block of a piece of writing, comma splices and fused sentences make you look like an amateur!
To fix the problem above, you could put a period after burst and begin finally with a capital F.