Explanation:

- Consider four consecutive numbers: \(x, x+1, x+2, x+3\).

- The average of these numbers is given as 64.5.

- The sum of these four numbers is \(4 \times 64.5 = 258\).

- Set up the equation: \(x + (x+1) + (x+2) + (x+3) = 258\).

- Simplify the equation: \(4x + 6 = 258\).

- Solve for \(x\):

- Subtract 6 from both sides: \(4x = 252\),

- Divide by 4: \(x = 63\).

- The numbers are 63, 64, 65, and 66.

- The largest number is 66.

Therefore, the correct option is:

- Option 4: 66