Certainly! Let's break down the sentence "Did Meta cook?" syntactically.

1.  **"Did"**:
    * This is an auxiliary verb, specifically a form of "do."
    * It functions as a modal auxiliary, indicating a question.
    * Syntactic category: Auxiliary Verb (Aux)

2.  **"Meta"**:
    * This is a proper noun.
    * It functions as the subject of the sentence.
    * Syntactic category: Noun (N)

3.  **"cook"**:
    * This is a verb.
    * It functions as the main verb of the sentence, indicating the action.
    * Syntactic category: Verb (V)

4.  **"?"**:
    * This is a punctuation mark.
    * It indicates that the sentence is a question.
    * Syntactic category: Punctuation (Punc)

**Sentence Structure:**

* The sentence follows a Subject-Auxiliary Inversion structure, which is typical for yes/no questions in English.
* The basic structure is: Auxiliary + Subject + Verb.
* In terms of phrasing, it is a verb phrase.

**Syntactic Tree (Simplified):**

```
   S (Sentence)
   / | \
  Aux NP VP
  |   |  |
Did Meta cook ?
```

**Analysis:**

* The sentence is a simple interrogative sentence.
* It asks whether Meta performed the action of cooking.
* The placement of the auxiliary "did" before the subject "Meta" is what creates the question.