I agree with Chad and Peachy, the sentence is awkward. It should read, 'what does she object to most about supermarkets'. I think your question is, why are there two prepositions, 'to' and 'about'? In this case 'to' is not a preposition, it is part of the infinitive, 'object to'. An infinitive is a verb plus 'to'. 'About' is a tricky word with several meanings. It can mean 'approximate', as in; he was about forty miles from home, or the apple cost about a dollar. It can also mean 'referring', as in; we talked about the weather, or he wrote an essay about eagles. Your own sentences could read, 'I found this sentence in a book', and, 'could somebody explain this sentence to me please'.

Well, we know she objects to supermarkets. We want to know what bothers her most, regarding (about) supermarkets. Maybe if we split the sentence like so... "What does she object most to / about supermarkets?" If you remove "about" you've accidentally answered your own question. If you remove "to" then that makes no sense. "Object to (something)" is the only way this verb works.

I can't answer this because I'm not wearing the festival costume, I really don't want to spoil it here, but I can't help telling you those are both my favourite flowers and colors!