Write the greatest 4-digit number of four different digits.

The digits available are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Thousands digit: The largest digit is 9.

Current digits used: {9}

Hundreds digit: From the remaining digits, the next largest is 8.

Current digits used: {9, 8}

Tens digit: From the remaining digits, the next largest is 7.

Current digits used: {9, 8, 7}

Units digit: From the remaining digits, the next largest is 6.

Current digits used: {9, 8, 7, 6}

Combining these digits in order, the greatest 4-digit number with four different digits is 9876.

Hence, the greatest 4-digit number with four different digits is 9,876.