This is an extremely clever question, and I think you got it right. The semishaded area on the lower left is 1/4 of the circle. The rest of the circle represents 3/4 of the circle. If you take 1/4 of the 3/4 that is left, you have the answer. So that makes your answer correct.
You should try to see what the actual answer is. It might be confusing so I hesitate to include it. 1/4 * 3/4 = 3/16. Is there any way to tell that what is in the dark blue region is 3/16 of the circle? I don't think so, not directly.
The only way you can get the answer is by doing what you did. Nice work.