Question 1026961
The sample space consists of all ordered pairs (d,c), where d = 1,2,3,4,5,6, while c = 1,2.

The values of X = d-c are then 0, 1, 2, 3, 4, 5, and 6.
X = 0 appears once,
X = 1 appears twice,
X = 2 appears twice,
X = 3 appears twice,
X = 4 appears twice, 
X = 5 appears twice,and 
X = 6 appears once.

Since all the values on the die are equiprobable, and likewise with the coin, the probability table for X is as follows

X     0       1        2      3      4       5        6
p(X) 1/12   2/12=1/6  1/6    1/6    1/6     1/6      1/12