I know that a multiple of 6 is also a multiple of both 2 and 3, so I can use the divisibility rules for those numbers to help me find the missing digit. For a number to be divisible by 2, it has to end in an even digit, so the possibilities for $\square$ are 0, 2, 4, 6, or 8. For a number to be divisible by 3, the sum of its digits has to be divisible by 3. The sum of the given digits is 5 + 2 + 2 + 8 = 17, so I need to add $\square$ to get a multiple of 3. I can try each of the even digits and see if they work. If $\square = 0$, then the sum is 17, which is not divisible by 3. If $\square = 2$, then the sum is 19, which is also not divisible by 3. If $\square = 4$, then the sum is 21, which is divisible by 3, so this is a possible answer. If $\square = 6$, then the sum is 23, which is not divisible by 3. If $\square = 8$, then the sum is 25, which is not divisible by 3. Therefore, the only digit that makes $52\,28\square$ a multiple of 6 is 4. 
The 5-digit number $52\,28\square$ is a multiple of 6.  Which digit is represented by $\square$?