If you multiply the four-digit number abcd by 4, the order of digits will be reversed. That is, abcd x 4=dcba. The digits a, b, c and d are all different. Find abcd. That means what numbers are abcd equal to?

The given is that A B C D x 4 = D C B A

Possible values of A are 1 or 2. It can't be 1 since the final result A is in unit place and 1 is not possible when we multiply any number by 4

2 B C D x 4 = D C B 2

It is clear above, that D = 8

2 B C 8 x 4 = 8 C B 2

Possible values of B should be 1 or 2

We try B=1

2 1 C 8 x 4 = 8 C 1 2

To find for C, you can use the equation:

(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420

Therefore,

C = 7

So, the number is 2178.