She couldn't hardly fit the book in her purse.

Double negative
incorrect intensive pronoun
slang

The sentence contains a double negative. "Couldn't hardly" is a combination of "could not" and "hardly," both of which convey negation. To correct the sentence, you could simply remove "hardly" to say, "She couldn't fit the book in her purse." This would convey the intended meaning more clearly.

The sentence "She couldn't hardly fit the book in her purse" contains a double negative. In standard English grammar, using two negatives in a sentence creates a positive meaning. Therefore, the correct version of the sentence would be "She could hardly fit the book in her purse."

There are no intensive pronouns in the given sentence. An intensive pronoun is a pronoun used to emphasize or intensify a noun or pronoun that is already present. Examples of intensive pronouns include "myself," "yourself," "herself," etc. Since there are no pronouns being emphasized in the sentence, there is no incorrect use of an intensive pronoun.

Lastly, the given sentence may contain elements of slang. Slang refers to informal language that is associated with a particular group of people or a specific context. However, without further context, it is difficult to determine if any specific slang terms are being used in the sentence.

The phrase "She couldn't hardly fit the book in her purse" contains a double negative. Using double negatives (in this case, "couldn't" and "hardly") cancels each other out and creates a positive meaning. So, the sentence could be rephrased as "She could fit the book in her purse."

To avoid using double negatives, you can simply use a single negative word such as "couldn't" without adding another negative word like "hardly." By doing so, the sentence would be grammatically correct and convey the intended meaning.

Regarding the other options, the phrase does not contain an incorrect intensive pronoun. Intensive pronouns are used to emphasize a noun or pronoun in the same sentence. There is no pronoun in this sentence that serves as an intensive pronoun.
Additionally, the phrase does not necessarily use slang. Specific slang terms can vary based on region or context, but the sentence itself does not appear to be using any slang.