Is this correct grammar The subject walked past the door?

Yes, "The subject walked past the door" is grammatically correct.

Here's why:

* Subject: "The subject" is the noun performing the action.

* Verb: "walked" is the past tense of the verb "to walk".

* Prepositional Phrase: "past the door" is a prepositional phrase acting as an adverbial, telling us where the subject walked.

The sentence is clear, concise, and follows standard English grammar rules.