Let's suppose they are in order smallest to largest:

__, __, __, __, __, __

Since the median has to be 8, and 6 is an even number,
choose the middle two numbers to have an average of 8.

For instance, 6 and 10 have an average of 8, since 

__, __,  6, 10, __, __

Now pick any two positive numbers for the first two which 
do not exceed 6, for instance, pick 4 and 5:

 4,  5,  6, 10, __, __

Now since the mean must be 10, the sum has to be so that when
we divide it by 6, we'll get 10.  That means that the sum must
be 60.  Adding the ones we have 4+5+6+10 = 25, so the last two
numbers must have sum 60-25 or 35.  So we pick two numbers 10 or
greater that have sum 35, say 15 and 20.

 4,  5,  6, 10, 15, 20

There are many, many, many, possibilities, for example

This one has the biggest standard deviation:

 1, 1, 8, 8, 8, 34 (the numbers are spread the most apart)

This one has the smallest standard deviation: (the numbers are closest together)

 8, 8, 8, 8, 14, 14

Here are some other possibilities:

 1, 1, 1, 15, 15, 27

 1, 4, 5, 11, 14, 25

 2, 3, 5, 11, 12, 27

 3, 3, 6, 10, 19, 19

In every case above the median is 8 and the mean is 10.


Edwin