OK, I'm thinking out loud here.

Looking at the thousands column:

D=4A+x, where x<4. A<3, if A=1, D=4+x; if A=2, D=8or9.

Looking at the ones column:

Since 4D=10y+A, A must be even, thus A=2 and D=8

Since x=0, looking at the hundreds column, C=4B+z<10, so B=1or2, but two is taken by A, so B=1 and C=4+z

Looking at the tens column:

B+10z=4C+3, or 1+10(C-4)=4C+3; 6C=42, thus C=7

4*2178=9712 QED