Every integer can expressed as product of several prime numbers.If an odd integer don't contain 3 as factor it is not divisible by 3.Therefore all odd numbers are not divisible by 3.

X=4Y  =>1000a+100b+10c+d=4000d+400c+40b+4a  =>3999d+390c-60b-996a=0  =>1333d+130c-20b-332a=0......(1)  d!=0;d=3 Ydoes not remain 4 digit number . Again d is even 4a is even.  Therefore,d=2 ; a=4d or 4d+1 i.e 8 or 9 but as least significant digit of 4a is 2 ;a=8.  Putting a,d in (1) we get 1333-1328=10b-65c=>13c=2b-1=>13 divides (2b-1) => b=7 =>c=1  So,Y=2178;X=4Y=8712.