The question says, "Which one of the following is an example of the kind of action that Burke feared would pose a serious threat to museums in his country?"
The relevant text to look at is the second paragraph, which discusses Burke's testimony. In particular, lines 15 to 21 mention Burke's fear: "otherwise, he said, other countries could seek to reclaim valuable art objects, no matter how long they have been held by the current owner or how legitimately they were acquired. Any country could enact a patrimony law stating that anything ever made within the boundaries of that country is its cultural property."
From this, we know that Burke is scared that without a statute of limitations, some country could make up a law that says that anything that was made there is their property, and then they could go after a museum in another country for having artwork that belonged to the country that made the law.
In the answer choices, we're looking for an example that illustrates this general idea.
(C) says "the passage of a law by another country declaring that all objects created by its aboriginal people are the sole property of that country." This is a great example of what Burke mentioned in the second paragraph as being his fear. Burke worried that if another country just made up a law about works created in it, it could claim possession of artwork in a museum in a different country. This is the correct answer choice.
Does this make sense? Let us know if you have any more questions!