Aset of 5 numbers has a mode of 12 a median of 11 a mean of 10 what could the numbers be?

The median is 11, so 11 is part of the data set. We have an odd number of values (5) which is why the median is part of the data set.

The mode is 12. The value 12 shows up the most times. Let's say it shows up twice. So far the data set is {11, 12, 12}

Let's introduce two more numbers x and y
The new data set is {x, y, 11, 12, 12}

Add up the five values and then divide by 5. We want this result to be equal to 10
(x+y+11+12+12)/5 = 10
(x+y+35)/5 = 10
x+y+35 = 10*5
x+y+35 = 50
x+y = 50-35
x+y = 15

So we don't know what x or y is, but we know that they must add to 15. So all you have to do is list two numbers that add to 15. One such pair is x = 6 and y = 9. Another pair is x = 7 and y = 8. There are infinitely many possibilities if you can use any real number. 

So one possible set is {6, 9, 11, 12, 12}
Another possible set is {7, 8, 11, 12, 12}