The steps are the same as 3 digit multiplication by 11.
Here is an example of 4 digit multiplication.
5763 x 11
The first digit becomes the first digit of the answer
5763 x 11 = 5 _ _ _ _
Adding the next two digits 5 + 7 gives 12. The second digit 2 in 12 becomes the second digit of the answer.
5763 x 11 = 5 2 _ _ _
Since 12 has two digits, we carry over the first digit 1 so 5 becomes 6.
5763 x 11 = 6 2 _ _ _
Adding the next two digits 7 + 6 we get 13. The second 3 in 13 becomes the third digit of the answer
5763 x 11 = 6 2 3 _ _
Since 13 has two digits, we carry over the first digit 1 so 2 becomes 3.
5763 x 11 = 6 3 3 _ _
Adding the next two digits 6 + 3 we get 9 which becomes the next digit of the answer.
5763 x 11 = 6 3 3 9 _
The last digit 3 becomes the last digit of the answer.
5763 x 11 = 6 3 3 9 3
Let me know if this example clarifies.