Böyle = このような、このように Öyle = そのような、そのように、あのような、あのように Böyle bir teklifi kabul edeceğini sanmıyorum. Böyle acıklı şeyleri ne diye yazıyorum. Ben öyle bir şey demedim. Bize öyle öğrettiler. İyi olduğunu sandık. このような問題の前例はない。Böyle bir sorunun benzeri yok. 君の年齢だったら、私もそう考えるだろうね。= Senin yaşlarındayken ben de öyle düşünürdüm.

'öyle' - like that 'böyle' - like this Öyle mi? - Really?

The difference between "böyle" and "öyle" The first difference between them is "near" and "far" Böyle is used for near activities Öyle is used for far - away activitie Example: You see your friend opposite (a bit far 4-5 metres) you who tries to repair his computer, and you understand that repairing way is not true. So you can say to him as "Öyle olmaz!" (means, you can't repair it like that way) You are with your friend, near you, you are together, and he tries to repair his computer, may be also you are looking his rearing way and understand that repearing way is not true: So you can say to him as "Böyle olmaz!" (means, you can't repair it like that way) The second difference between them is "now" and "past" Böyle is used for "present continious, today, at that our, at that moment..." Öyle is used for "past...yesterday, last year, last century..." Example: You had a busy day and that night you say your friend that "I didn't expect such a busy day, but I had." Böyle yoğun bir gün yaşamayı beklemiyordum. You had a busy yesterday and you say your friend about yesterday that "I didn't expect such a busy day, but I had." Öyle yoğun bir gün yaşamayı beklemiyordum ama yaşadım. The third difference between them is "tangible" and "intangible" Böyle is used for "tangible" situations Öyle is used for "intangible" situations Example: You meet your girl friend with your mom and you say your mom "Have you ever seen such a beauty girl mom?" Daha önce böyle güzel bir kız gördün mü anne? You talked about your mom whom you saw a girl you met at that day and yu couldn't forget, and you laud her beauty to your mom "Mom! It's a lovely girl that I can't describe her beauty" Anne! Öylesine güzel bir kızdı ki anlatamam. But please don't forget! Sometimes there are exceptionals situations...

Şöyle böyle.「まあまあだ。」 Öyle mi ?「そうですか。」（相槌） şu anda 「今、目下」 -- Şu anda ne yapıyorsunuz? -- Kitap okuyorum.

[böyle] demek senin gösterdiğin örnek. [öyle] demek ise başkasının yaptığını örnek göstermek gibidir. ;) kolay gelsin