The correct answer is B. I subjected my mind to hard thinking.
A is incorrect because consulting several people does not necessarily involve hard thinking.
C is incorrect because reading a number of books does not necessarily involve hard thinking.
D is incorrect because brainwashing several experts does not necessarily involve hard thinking.
E is incorrect because using common sense does not necessarily involve hard thinking.
The phrase “rake my brains” means to think very hard about something. It is often used to describe the process of trying to solve a difficult problem. In this case, the speaker is saying that they thought very hard about the problem in order to solve it.