Find the four digit number

4(1000a+100b+10c+d)=1000d+100c+10b+a
this gives us...
1333a+130b-20c-332d=0
now we know that since a,b,c,d are digits...they lie between 0 to 9...
max value of 20c+332d can be 3168....therefore a cant be more than 2...if a is 1 then the unit's digit doesnt satisfy the expression for any integer value of b,c,d...
therefore a has to be 2...
since a is 2....b can be 1,2 or 3...
now checking for them and solving....we get a=2,b=1,c=7,d=8....