Right answer: dice
This is a sentence written in present tense (indicative) with the 3rd person in singular he (él), which is Juan Carlos. Hence, the verb decir is conjugated as él dice (he says).
Then the complete sentence is:
Juan Carlos dice que va a llover.
Juan Carlos says it is going to rain.
The other options are incorrect because:
Oye (he hears) and oyen (they hear) does not match with the context of the sentence
dicen (they say) is conjugated with the 3rd person in plural ellos (they) and is not in accordance with the subject of the sentence.
