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Answer: One million minus 4
Dividing by 6
$$\begin{align}166666&\text{ remainder 4}\\
6\overline{)1000000}&\end{align}$$ So $4$ less than $1000000$ is a multiple of $6$
Looking for multiples of 6
In order to be a multiple of 6, a number must be both even and a multiple of 3. Of the numbers given, only (b) 999 998 and (d) 999 996 are even.
For a number to be a multiple of 3, the sum of its digits must also be a multiple of 3. From this, we see that, of these two, only (d) 999 996 is a multiple of 3. Hence (d) is the only multiple of 6 here.
Almost a Million
Age 11 to 14
ShortChallenge Level 
Answer: One million minus 4
Dividing by 6
$$\begin{align}166666&\text{ remainder 4}\\
6\overline{)1000000}&\end{align}$$ So $4$ less than $1000000$ is a multiple of $6$
Looking for multiples of 6
In order to be a multiple of 6, a number must be both even and a multiple of 3. Of the numbers given, only (b) 999 998 and (d) 999 996 are even.
For a number to be a multiple of 3, the sum of its digits must also be a multiple of 3. From this, we see that, of these two, only (d) 999 996 is a multiple of 3. Hence (d) is the only multiple of 6 here.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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