Step 1: Understand the idiom.
The phrase "racked my brains" means to think hard and strain your mind to find a solution or recall something. It does not refer to reading, asking others, or trusting instinct. It points only to intense mental effort by the person alone.
Step 2: Check each option against this meaning.
Option A says the person read many books, but the idiom is about thinking, not reading. Option B says the person asked others for help, but racking your brains means solving it yourself, not consulting people. Option C says the person used commonsense, which is a much milder idea than the intense effort the idiom carries.
Step 3: Match the closest meaning.
Option D says the person subjected the mind to hard thinking. This matches the idiom exactly, since racking your brains is about pushing your mind to work hard on a problem.
Final Answer:
The idiom "rack one's brains" means to think very hard, so option D gives the correct restatement. \[ \boxed{\text{D}} \]