i do not think i m capable of answering this question it looks really hard but i gonna try to do my best . i found some sentences from Turkish dictionary Ben ÖYLE bir şey demedim. (i did not say anything LIKE THAT) BÖYLE bir teklifi kabul edeceğini sanmıyorum . (i do not think that i will accept an offer LIKE THIS) Şöyle söyleme. (dont say LIKE THIS) in this case we can say : Böyle söyleme , but we cannot say Şöyle bir teklifi kabul edeceğimi sanmıyorum. and also we can say : ben böyle bir şey söylemedim. another ex. öyle yap.(your friend says i know how to do it and your reply is okay then öyle yap) böyle yap.(your friend says i dont know how to do it and your reply is i know how to do it so do it like this) şöyle yap. (almost same with böyle yap but it is also includes little bit suggestion) i hope it helps

ı try give example sentences BÖYLE: BÖYLE YAPMA,ŞÖYLE YAP BÖYLE DEME ŞÖYLE DE BÖYLE SÖYLEMEN DAHA İYİ ŞÖYLE YAPMAN DAHA İYİ SİMİLAR TO BÖYLE YAPMAN DAHA İYİ I hope you can understand

Watching this with interest. Hope someone comes along and answers this.

I know they mean "like this" or "like that". And I am guessing they work the same as o, bu, şu. O=that, öyle=like that....bu=this, böyle=like this...şu=that(one or over there), şöyle=like that (one or over there) I hope a native speaker can let us know exactly. :)