Translation:I do not wear hats very often.
Good point. We all do this. But in all fairness, Duo should be better about staffing up contributors to mark those answers as correct. We get spurts of emails with notifications of a few corrections, but in all languages here I've seen many bad answers that had not been addressed by Duo for months or years.
Also, for me, the discussion is helpful for me to see when a question doesn't allow obvious answers. It's helpful to see what others are writing, and sometimes just amusing. As good as Duo is, sometimes it's really dumb, and it makes for an amusing little break sometimes to commiserate in the forums.
Things you wear and their respective verbs
着る 【き・る】- to wear Clothes that cover your-upper body and more (シャツ、ブラウス、ジャケット、ドレスなど)
履く 【は・く】- to wear Clothes for your lower-body and feet （ずぼん、ジーンズ、靴下、ブーツ、靴など）
被る 【かぶ・る】 – to cover Items that go over such as hats （帽子など）
かける – to hang Items that hang such as glasses and sunglasses （メガネ、サングラス）
巻く 【ま・く】 – to wrap Items that wrap around such as scarves （スカーフ、マフラーなど）
締める 【し・める】 – to tie Items that fasten such as neckties and belts （ネクタイ、ベルト、帯など）
着ける 【つけ・る】 Items that attach such as wigs and earrings （かつら、イヤリング、ピアスなど）
はめる – to insert Items you stick your finger into such as rings （指輪）
する – to do A generic term for things like gloves, earrings, necklaces （手袋、イヤリング、ネックレス）
I can hear it. It's a very soft 'b' at the start, followed by a strong OH!!! which is why I'm guessing it sounds like O at the start to you instead of BO. Try listening to it a bunch of times and listen for the 'b' at the start. It's just a matter of getting used to listening and understanding and familiarisation with the language - everything sounds faster when you don't understand it.
I just tried this answer and it was marked as wrong, so I've reported it.
It isn't grammatically incorrect - the words "often" and "a lot" are typically used interchangeably in casual English.
Duo may be trying to emphasize the difference between "often" (frequency) and "a lot" (volume). Or in this case, あまり meaning "not often".
Or they just haven't added it to the list of acceptable answers.