To find out how long Patricia studied for her science test, we need to calculate half of the time she studied for her Social Studies test.
Patricia studied 412 hours for her Social Studies test. Therefore, for her science test, she studied:
\[ \frac{412}{2} = 206 \text{ hours} \]
However, it seems that the options provided (2 1/2 hours, 2 1/4 hours, 9 hours, 1/2 hour) do not match with the calculation. If you have more information or perhaps if there's a typographical error in the question, please provide that for further assistance!