a has to be either 1 or 2 as multiplying by 4 keeps the number 4 digits.

(if a= 3 then quadrupling that number would be >12000 (5 digits) )

if a was 1 then d would have to be 4 so our number abcd would be:

1bc4 and its reverse would be 4cb1 which cannot be as an integer multiplied by 4 has to be even.

Therefore a has to be 2.

Making d = 8.

When multiplying 2bc4 x 4 to be 8cb2, b and c cannot be too large as multiplying by 4 would then make the thousands place >8.

For example if b = 3 then even the lowest # in the 2300s, 2300 x 4 = 9200 would be too large as a = 9.

So b must be 0, 1 or 2

b cannot be 0 as 20cd x 4 = dc02 and multiples of 4 always with the last two digits as a multiple of 4.

b cannot = 2 since a is already 2 so b must = 1!

c cannot be 1, 2, or 8 as they have already been used

So abcd is now 21c8 x 4 = 8c12

If c = 0, 2108 x 4 does not end in 12

If c = 3, 2138 x 4 does not end in 12

If c = 4, 2148 x 4 does not end in 12

If c = 5, 2158 x 4 does not end in 12

If c = 6, 2168 x 4 does not end in 12

If c = 7, 2178 x 4 DOES end in 12

If c = 9, 2198 x 4 does not end in 12

c cannot be 1, 2, or 8 as they have already been used

2178 x 4 = 8712