1. Which fund-raising event did he hold?

2. He held a fund-raising event for poor children?
[#2 is the answer to #1. 'For poor children' is an adjective phrase, which modifies 'event.']

3. Why did he hold a fund-raising event?
4. He held a fund-raising event for poor children.
[#4 is the answer to question 3. So in this case 'for poor children' is an adverb phrase, which modifies 'held' What about my explanation? #2 or #4 has ambiguity, I think.]

I've answered this before, right?

In both sentences, "for poor children" is an adjective phrase, describing "event."