What is an example of a hyperbole in the book Gathering Blue?
Well, hyperbole is just another word (a literary word, mind you) for exaggeration. It is pretty easy to find, both in this book and in others. However, please realize that it is an error to ask for "a hyperbole." No need for the article "a" there. Just look for an example of hyperbole. We can find a good one in the following quotation.
Over and over. They be making me remember everythings. Me old songs, they just be natural. But now they be stuffing new things into me and this poor head hurts horrid.
Now, amid the stunning vernacular, let's explain the quotation and then explain why it's hyperbole and exaggeration. The character of Kira is frustrated and tired. Why? She is being forced not just into her own fond memories but into "new things" that are implied here to be "not natural." These new thoughts and forced ideas, in addition to not being natural, are causing her frustration.
In regards to the actual hyperbole of the quotation, it is within the last phrase: "they be stuffing new things into me and this poor head hurts horrid." No one is actually "stuffing" thoughts into her head (even though brainwashing is a real thing). Therefore, this is exaggeration. Further, saying her "head hurts horrid" is an exaggeration as well. It is an exaggerated expression of frustration. Kira doesn't actually have a headache here, she is frustrated in her mind at all the things she has learned. This is true hyperbole.