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To find the price per pint, we need to convert the volume of the mouthwash from cups to pints.
1 cup is equal to 0.5 pints.
Therefore, 4 cups is equal to 4 * 0.5 = 2 pints.
Now, we can calculate the price per pint by dividing the cost of the mouthwash by the number of pints:
$9.96 / 2 = $4.98 per pint.
So, the price per pint of the mouthwash is $4.98.