It seems that the sentence is incorrect, vermeiden doesn't mean to prevent: http://en.pons.com/translate/german-english/vermeiden
On the other hand, verhindern: http://en.pons.com/translate/german-english/verhindern
If we assume that vermeiden usually means to avoid AND verhindern usually means to prevent, then I can remember this by noticing the connection between to hinder and to prevent. In fact, hindern can mean to hinder, and we know that in German the prefix ver- is sometimes an intensifier. So if you intensify hinder you get prevent.
Pop-up hints are suggestions (possibilities) offered for a word without any consideration of context or the sentence in which the word appears. Usually, among the hints is an answer that Duolingo should and will accept. But you can't expect every choice offered will be accepted. And usually, but not always, the rejection of a particular hint is because that choice is indeed incorrect for the sentence in which it appears. The pop-ups are not a cheat sheet. You still have to choose the right word for the given sentence.
In the sentence here, "avoid" is a better answer, and neither "will not prevent" nor "am not going to prevent" should be accepted.
"Meiden" usually refers to avoiding things or persons, "vermeiden" usually refers to avoiding something to happen. "Ich meide ihn" = I avoid him. "Ich meide Höhen" = I avoid heights. "Ich vermeide es, ihn zu treffen" = I avoid to meet him. However, "meiden" is not a very common word in spoken everyday language, and you may well hear "vermeiden" instead (or, else, "aus dem Weg gehen", "umgehen", etc.).