Here are all the possible rolls. I have colored all the 
ones red that are either doubles or have a sum of 6.

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
 
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
 
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
 
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
 
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Count how many red ones there are.  That will be the numerator of
the probability.

Count how many possible rolls there are.  That is, count all of them
whether they are red or black.  That will be the denominator of
the probability.

Put that numerator over that denominator and reduce the fraction.

That reduced fraction will be the answer.

Edwin