Which sentence is written correctly? The, local market, has the freshest produce and meats in town. Takeko, a painting student o
ffered to help with a sculpting demonstration. The store offers, many products, which can be personalized with your initials. Sarah, Matt's wife, works as a business software developer
The sentence that is written correctly is the one that reads as follows: Sarah, Matt's wife, works as a business software developer. The NP (noun phrase) "Matt's wife" is between commas because it represents information which is not necessary to understand the meaning of the sentence. You could simply drop it and the sentence would still make sense (Sarah works as a business software developer). It only adds information to identify Sarah as someone's wife.
In the first sentence, the determiner (the) is separated from its noun phrase (local market) so the sentence is not correct. Then, the second one, lacks a comma after "student" for it to represent the same use of this punctuation mark as in the last example. Furthermore, in the third sentence the comma after "offers" is separating the verb from its D.O (direct object). That is why it is not correctly written.
