a favorable opinion

It means holding a positive view of the subject--which, by the way, is not evident from the context you have provided.

This sense...

fansy:
I am not sure where you are going with these requests, are we doing your homework for you?
However; let's start with the simple lack of punctuation in your quotes. The English language relies heavily upon the proper use of punct. Our punct. defines the nuance(s) of the context, and gives proper direction towards the full meabing of a bodied script.

Try this:
Other countries where positive views dropped significantly include: India (56 percent, down from 71 percent); Russia (43 percent, down from 52 percent), and Indonesia (30 percent, down from 38 percent). In Turkey; only 12 percent said they held a favorable opinion, down from 23 percent last year.

@ include - a colon ( : ) is required here because you are including a list.
@52 percent - a comma (,) is all that is required here because you are continuing that list.
When punctuation is used correctly, most questions are (as yours) easier to answer. " Favorable" in this context is used to define Turkey's response to a poll taken on a undefined subject.

A2k is a useful resource for many language students. Some chunks and idioms are not always apparant from context or dictionaries. We are helping with understanding usage, rather than doing homework. Glad to see you have joined in the effort.