Final answer:
The sentence requires commas to properly set off the nonrestrictive clause and before the coordinating conjunction linking two independent clauses.
Step-by-step explanation:
The question is asking whether the sentence requires a comma. The correct sentence with appropriate punctuation should be: "Beth, my two-year-old, is very curious, so I have to keep a close eye on her." Commas are used here to set off the phrase 'my two-year-old' which is a nonrestrictive clause providing additional information about Beth. This clause could be omitted without changing the essential information of the sentence, which is a characteristic of nonrestrictive clauses. The second comma comes before the coordinating conjunction 'so' because it introduces a second independent clause which could stand as a sentence on its own.