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Answer:
The answer is hyperbole.
Explanation:
It's a familiar question.
Also, Hyperbole is an exaggeration. The most blatant display of exaggeration here is the author's description of her laughter.
The following lines show this:
"...and it nearly killed her laughing"
"...she laughed herself lame--she did, indeed;"
She couldn't have possibly laughed herself lame of course but the hyperbole is used in showing how hard she must have laughed at what he was telling her.