Paul didn't tell me ... about his troubles.

This is a sentence in English that requires a word to complete the meaning. The sentence structure "didn't tell me ..." often pairs with words that indicate negation or indefiniteness.

• nothing: "Paul didn't tell me nothing about his troubles." This is a double negative, which is grammatically incorrect in standard English.
• something: "Paul didn't tell me something about his troubles." This is grammatically correct, but the meaning is that he withheld some information.
• anything: "Paul didn't tell me anything about his troubles." This is grammatically correct and implies that he told me no information at all. In negative sentences, 'anything' is typically used instead of 'something'.

Given the common usage in English, 'anything' is the most appropriate word to complete the sentence to indicate that Paul told me no information about his troubles.

Answer: anything