if A B C D represents a different digit what is the value

if A B C D represents a different digit what is the value of A

2A
+ B2
______
D 2 C

there are two reasons. first, the unit digit of sum of B and 2 is already given as 2. to have 2 as unit digit of the sum of B+2, we have to have 9 as the value of B.
Second, we know A,B,C, and D, all, are different digits and D is 1 (because no one digit two integers have sum more than 19) and it must be 1. when D is 1, then 2+A must not be 11 and can not be more than 11. to have B+2 as 12, A+2 must be two digit integer which can only be possible when A is 8. when A is 8, B cannot be 8 because A,B,C, and D, all, numbers/integers are different digits . therefore B must be 9.