Answer:
The number is 2178, multiplied by 4 gives 8712.
Step-by-step explanation:
Let us say the number is written as abcd
.....(1)
When you multiply it by 4, it gives dcba 
Now,
We get;

=> 
=>
......(2)
Now, we can relate few properties:
The first digit is a quarter of the last one as d=4a .
or 
or 
The second digit is one less than the first.

Now, from equation 2, we get

Replacing b and d, we get

=> 
=> 
or, 
There is only one single digit integer solution.
c = 7; a = 2
Now,
=1 and d =4(2) =8
Hence, 2178 is the number.
And we can see that 