To fix the punctuation and capitalization errors in the given sentence, you should make the following corrections:
Peeta Mellark told stories about the "puppy who could speak," but his friend did not believe him.
Explanation:
1. Capitalize the first letter of the sentence.
2. Remove the comma after "the" before the opening quotation mark.
3. Add a comma after "speak" within the quotation marks.
4. Ensure that the punctuation marks are placed correctly within the quotation marks.