What examples of hyperbole appear in the poem "the mother" by Gwendolyn Brooks?
With its title purposefully written in all lowercase letters to emphasize humility, "the mother" is a poem about a woman who acknowledges the children she would have had if she had decided not to abort them.
In such a dramatic and emotional situation, some hyperbole (or exaggeration for effect) might be expected, but isn't truly necessary: when the speaker simply states the reality of her situation as an impoverished woman with deep regrets, it's dramatic enough on its own.
For example, the second stanza is full of highly poignant statements addressed to the unborn children, like "If I poisoned the beginnings of your breaths." Whether that is hyperbole or not is arguable; "poisoned...your breaths" could be a literal description of the abortion procedure coming from an uneducated speaker who doesn't quite understand all the medical details. Earlier in that same stanza, the speaker also says: "If I stole your births and your names." Is this language figurative and dramatic? Yes. Hyperbolic? Not really. The decision to abort really did negate the births and names of the would-be children.
Here is the only instance of definite hyperbole that does appear in the poem: "Return for a snack of them, with gobbling mother-eye."
Here, "them" means "the children." To say that the speaker could never "snack" on her children with a "gobbling" eye is an exaggerated way of expressing a mother's zealous affection for her children. You know how people sometimes say "You're so cute, I could just eat you up" to little kids? The same idea appears in this poem. It's hyperbolic because it elevates the idea of gazing lovingly at your kids and perhaps hugging and kissing them to the idea of actually consuming them. That's hyperbole.
Again, other dramatic statements in the poem may be argued to be hyperbolic, but the statement above is the only obvious, completely defensible instance of hyperbole.