Which detail shows that Kamen's light-controlled systems were very good? Kamen was introduced to a man who sold audio-visual equipment for big light and music shows. When he was sixteen, Kamen spent all summer building high-powered light-controlled systems. One of his inventions was used in theaters, the Museum of Natural History, and the New York Planetarium. To make one of his devices, he bought every kind of electrical equipment that he could find.

Even though it is possible to answer this question without the passage to which it refers, I will add it here to make answering easier:

Then I heard about a summer job through my uncle who was a dentist. He introduced me to one of his patients who had a business selling audio-visual equipment for big light and music shows. He was looking for some new, better equipment. I spent all summer when I was sixteen building high-powered light-controlled systems that synchronized many Kodak projectors at once, as many as sixty-four to 120 of them, and reduced the cumbersome machines from the size of a refrigerator to the size of a toaster. Not only was this invention used in theaters, but it was sold to the Museum of Natural History and the New York Planetarium to project views of the heavens on the ceiling. To make this new device I had bought every kind of electrical equipment I could find, and still had money left over.

The detail that shows that Kamen's light-controlled systems were very good is:

C. One of his inventions was used in theaters, the Museum of Natural History, and the New York Planetarium.

Explanation:

If Kamen's systems were not good, they wouldn't have been used at all, no matter how much time and money he had spent developing them.

The proof that they were good can be found in the line where it is said, "Not only was this invention used in theaters, but it was sold to the Museum of Natural History and the New York Planetarium to project views of the heavens on the ceiling." To be used in places such as the Museum of Natural History and the New York Planetarium, the systems must have had excellent quality. At those places, exhibitions are taken seriously, and they would have invested in good equipment and systems to make sure the quality was the best they could get.