The largest 4-digit number using any one digit twice from 5, 9, 2, 6 is
9652
9562
9659
9965
Step 1: Write the digits you have: \(9,\;6,\;5,\;2\).
Step 2: To make the largest number, we want the biggest digits at the left. So compare them: \(9 > 6 > 5 > 2\).
Step 3: The question allows repeating one digit. Repeating the largest digit makes the number bigger. The largest digit is \(9\), so we repeat \(9\).
Step 4: Put the digits in order with the repeated \(9\) on the left: \(9,\;9,\;6,\;5\). This forms the number \(9965\).
Therefore the correct answer is 9965.