Both *four-door car* and *four-doored car* are correctly constructed according to English grammar rules. Which one is more idiomatic based on actual usage is a separate issue.

The use of a phrase *four-doored* car does not necessarily imply the existence of a verb *to door.* English *-ed* has multiple functions. It can form the simple past tense of a verb, as in *They proved it.* It can form the past participle of a verb, as in *I have watched it before.* Some adjectives, such as *excited,* are derived from a verbal past participle ending in *-ed.* But a third function of *-ed* is forming adjectives directly from nouns (or nominal phrases) with the meaning "possessing [noun]".

Some examples: *small-minded, two-faced, cross-eyed, brown-haired.*

These are all idiomatic and usual, even though it is not usual to say *"They are minded small", *"They are faced two", "They are eyed cross", *"They are haired brown". Also, there is no implication that the state is a result of some change, as there often would be with a participial adjective (describing someone as *brown-haired* does not imply that their hair became brown after previously being a different color).

The Oxford English Dictionary has a separate entry for this use of *-ed,* which says the precise details of the etymology are unclear. Some quotations:

- > In modern English, and even in Middle English, the form affords no means of distinguishing between the genuine examples of this suffix and those participial adjectives in *-ed* [...] which are ultimately [from] nouns through unrecorded verbs

- > The suffix is now **added without restriction to any noun** from which it is desired to form an adjective with the sense ‘possessing, provided with, characterized by’ (something); e.g. in *toothed, booted, wooded, moneyed, cultured, diseased, jaundiced,* etc., and in parasynthetic derivatives, as *dark-eyed, seven-hilled, leather-aproned,* etc.


- > **Groundless** objections have been made to the use of such words by writers unfamiliar with the history of the language