To solve this question, let's analyze each clue one by one:
Audrey likes neither soccer nor football.
From this clue, we can deduce that Audrey does not like soccer or football. Therefore, Audrey's favorite sport is either kickball or tennis.
Danny used to like football and kickball best, but he has changed his mind.
According to this clue, Danny used to like football and kickball the most, but he has changed his mind. This means he no longer likes football or kickball. Therefore, Danny's favorite sport is either soccer or tennis.
Neither of the boys here likes soccer best.
This clue tells us that none of the boys (Robert or Danny) prefers soccer the most. This eliminates soccer as a possible favorite sport for both Robert and Danny.
Based on the given information, we can conclude that Audrey's favorite sport is either kickball or tennis, and Danny's favorite sport is either soccer or tennis. Since Danny used to like football and kickball but has changed his mind, we can infer that Danny's current favorite sport is tennis.
Therefore, the correct answer is D) Tennis.