What 4 digit number dcba equals abcd multiplied by 9?

dcba = 9 x abcd

dcba/9 = abcd

Since the quotient is also a 4 digit number, then d in order to be divided by 9, must be the biggest digit which is 9. So that d = 9 and a = 1. The same way for other digits...

So that we have:

dcba = 9 x abcd

9999 = 9 x 1111