In the example sentence (according to Chinese grammar wiki):
In these cases, all use 的 before a noun, once it moves before the verb. The original sentence does not use 的 to modify the noun (e.g. 你做菜做得很好。).
But I feel I have also seen such sentences without 的 modification, for example:
Or the sentence that made me determined to open this question:
Maybe syllables are also taken in consideration here. 你中文说得很好 sounds more natural than the others, as those nouns are just one character.
So is it acceptable or not to omit 的 here? Or is it grammatically wrong but used commonly?