There is a three-digit number that's a multiple of four. If you switch it's first and last digits, it's still a multiple of four. It's middle digit alone is odd. Which of these can be the first digit?

A number is divisible by 4 if its last two digits are divisible by 4. If the middle digit is odd (1, 3, 5, 7, 9), we need the first and last digit to form a two-digit number divisible by 4. Testing first digits: if first digit is 2, and middle is odd (say 1), we need 2X to be divisible by 4 where X is any digit. For 24, 28, etc., this works. First digit 1, 3, 4 don't work consistently with all odd middle digits.