How do you like this hat? (RHD)
The example’s ‘how’ is included in the denotation of ‘to what extent or degree’ (here, adverb how#2 in its online version). But when I look up Cambridge, it seems to be ‘used when asking someone for an opinion.’ OALD also seems to have the opinion as in: How did you like Japan (= did you find it pleasant)? In OALD, ‘like’ having this meaning, to find something pleasant, ‘how’ seems to be that it’s a kind of dummy - pleonastic? I don't find proper words - word: I mean, without ‘how’ it can make sense.
It’s very difficult to understand the ‘how,’ so I asked the Korean interpretation to a Korean language institute - I asked about this sentence: “How do you like this dress?” (Of course, it was Korean sentence - 어떻게 이 옷 마음에 들어?” not English -- it's not a place for asking foreign languages, only for my own tongue, so it would not be directly applied -- I tried this to understand the how indirectly from my language for I don’t understand the how in English way.). They say the Korean ‘how’ (어떻게) in the case is a kind of interjection, used colloquially. When I interpret the example from RHD, based on the institute’s Korean word explanation, I guess it would be making sense in English, too. I’m afraid if I could deliver what I think well, but what do you think of the ‘how’?