The first and fifth digit are the same because "twice the second" 
and "double the second" mean the same.  

So we have one of these four possibilities:  

A    8 4 _ _ 8    which has sum of digits 8+4+8=20
B    6 3 _ _ 6    which has sum of digits 6+3+6=15
C    4 2 _ _ 4    which has sum of digits 4+2+4=10
D    2 1 _ _ 2    which has sum of digits 2+1+2=5

the third is half the fourth, so we must fill in the two 
remaining blanks with one of these pairs of digits

0&0, 1&2, 2&4, 3&6 or 4&8, 

which have sums 

0+0=0, 1+2=3, 2+4=6, 3+6=9, 4+8=12.

The sum of all five digits must be 21.  Therefore:

A is ruled out because we cannot add 0,3,6,9 or 12 to 20 and get 21.
B is possible because we can add 6 to 15 and get 21.
C is ruled out because we cannot add 0,3,6,9 or 12 to 10 and get 21.
D is ruled out because we cannot add 0,3,6,9 or 12 to 5 and get 21.

So B is the only possibility and the 3rd and 4th digits are 2&4.

Answer: 

      6 3 2 4 6
 
Edwin