We can solve this together! We're beginning with 7743 and removing 129 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 3 in column 1 and get -6.
We add -6 to 10 and get 4 as the first digit of the result.

Step 2: We'll start by subtracting the digit 2 and the borrow 1 from 4 in column 2 and get 1.
1 is the next digit of our result.

Step 3: We'll start by subtracting the digit 1 and the borrow 0 from 7 in column 3 and get 6.
6 is the next digit of our result.

Step 4: We'll start by subtracting the digit 0 and the borrow 0 from 7 in column 4 and get 7.
7 is the next digit of our result.

So, 7743 - 129 = 7614.