6' == double head high. Anything from 6' up to a few feet higher (on the face) is DOH, therefore 6-8' is DOH. A straight 6' is easy, because it's two 6' people high. It's the overhead part that makes it 6-8'.
Same as 3' is head high, but 4' is overhead. DOH is just double 4'.
And I forgot the special case you sometimes see - 18'. Sometimes you see 15-18', which is when it's bigger than 15' but doesn't warrant the full 20' call. However, you're not allowed to use 18' by itself

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Generally as it gets bigger you use more of a range, because you get bomb sets and solid waves in between so you call them both as the range because even the smaller ones are significant. On smaller days you don't care about the in betweeners because only the sets are any good so it's more common to say it's 1' or 2' or 3' or 4'. It's only really when it gets bigger than that that you start using ranges. Or if you're unsure such as in the pictures that prompted the thread.
You might use a range if you're describing e.g. a whole day when the swell jumped, but that'd be part of the description too and would therefore emphasis how conditions changed.
To those that say it doesn't matter etc, it does if you're describing it to mates etc. E.g. if it's under 6' I'm going to treat it as fun, consequences not high. 6-8' is getting serious and I'd want to make sure I bring my A game and have a plan. 10' and it's very serious and you want to take things very carefully and have the right preparation and equipment. If someone told me it's 10' and they're talking some arbitrary face measurement system and I turn up fully psyched up with a gun, I'm going to be pretty annoyed when it's a playful 5' in reality.