intuitive response
ABCD=D*10^0+C*10^1+B*10^2+A*10^3
working out the conditions all the solutions must satisfy the next formula
A*10+D=9*(B-C) ,
for example 1978 is one of them.
I suggest to start from right B-C=2,3,4,...,9 and to find A and D,
form here a simple counting argument...