I suppose "when" asks for "will" instead of "would" plus a change of word order:
"When do you think will the Philippines host the Olympic Games?"

Thanks :D

The word order is wrong...
I would say: When do you think the Philippines WILL host the Olympic Games?

Sorry, mervert, I gave you the wrong advice earlier.

@arnxy20
On second thoughts it is still a question and not reported speech like "He wants to know when the Philippines will host the Olympic Games."
I think of it like "When - do you think - will the Ph host ..."
Google search "when do you think will" gives me dozens and more positive examples.
Could it be your version is the more colloquially used one?

Thank you, CK, for coming back.

I had the feeling that there were not enough "natives" around. Too few people commented on English sentences. It might be a wrong feeling that I had but I kept stumbling over incorrect or unidiomatic sentences "all the time" without them having been challenged. And some of them are at this moment sinking to the bottom of the Tatoeba ocean. Good luck to them.

"When do you think the Philippines will host ..." is the correct English expression.