Question
Write: The largest.

Answer

To write the greatest $6-$digit number having four different digits, we will have to use four largest digits.
Clearly $9, 8, 7$ and $6$ are four largest digits.
In order to write the largest $6-$digit number using digits $6, 7, 8$ and $9,$
we put the largest digit $9$ at the place having the highest place value.
The smallest digit $8$ is put at the hundred's place,
the smallest digit $6$ is put at the right most place i.e. at unit's place and the digit $7$ is put at the ten's place.
All other places are filled by $9.$
Hence, the required number $= 999876.$

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