Write the greatest six-digit number using four different digits.

For the greatest 6-digit number using exactly four different digits, the digits at the higher places should be as large as possible.

Use the digit 9 as many times as possible. With 4 different digits in 6 positions, use 9 three times and the next three largest different digits 8, 7, 6 once each.

Total digits used: 9, 9, 9, 8, 7, 6 — four different digits (9, 8, 7, 6).

Arranging in descending order: 9, 9, 9, 8, 7, 6.

Hence, the greatest 6-digit number using four different digits is 9,99,876.