Araucaria's answer to the following ELL question ("Why is “letter” not plural in “two letter words”?") brought up an interesting issue that I am still unsure about. What is the internal syntactic structure of modifiers like "two-letter" (in "two-letter word") or "five-mile" (in "five-mile run")?
Araucaria left a comment saying
H&P call them compound adjective constructions
While BillJ thought
I think "three-letter" is a noun-centred compound noun (det+noun) as attributive modifier of "word" in your example. I know dictionaries are unreliable, but they all give "four-letter" as a single noun in "four-letter word". The fact that it is hyphenated is an indication that "four-letter" is single lexeme, not a syntactic construction of modifier + noun (see CGEL p1644) [...] If the main component of a compound word is a noun, then the word can only be a noun. There is nothing adjectival about "three-letter" in "three-letter word". "Three-letter" is a noun-centred compound noun modifying "word".
I am not convinced hyphenation practices are relevant, since not everyone uses hyphenation in these circumstances anyway. Also, entire sentences or prepositional phrases can be hyphenated when they are used as preposed attributives, but I don't think that this means that they change their part-of-speech to become adjectives.
At least, it seems to me that Benjamin Bruening says these are syntactic compounds in The Lexicalist Hypothesis: Both Wrong and Superfluous, giving the following examples:
(1) a. I gave her a don’t-you-dare! look.
b. She baked her fiance a sweet I-love-you cake.
(I also found some other papers mentioning "phrasal compounds" like this; here are the download links: https://is.cuni.cz/webapps/zzp/download/130072761/?lang=en, ling.auf.net/lingbuzz/000599/current.pdf)
So, what evidence is there about the syntax of this construction? Should "two-letter" etc. be analyzed as compound nouns, compounds that are adjectives, noun phrases, or what?