Answer:
0000, 0770, 1001, 1771, 2002, 2772, 3003, 3773, 4004, 4774,
5005, 5775, 6006, 6776, 7007, 7777, 8008, 8778, 9009, 9779
Step-by-step explanation:
A 4-digit palindrome is of the form xyyx, so has the value 1001x +110y. 1001 is divisible by 7, but 110 is not, so y must be divisible by 7. The only two single digit numbers divisible by 7 are 0 and 7.
The numbers you seek are of the form x00x, or x77x, where x is any single digit. The 20 possibilities are listed above.
