Let's get this math done. We have 68626 and 12629, and we're going to subtract the second number from the first.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 6 in column 1 and get -3.
We add -3 to 10 and get 7 as the first digit of the result.

Step 2: We'll start by subtracting the digit 2 and the borrow 1 from 2 in column 2 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

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

Step 4: We'll start by subtracting the digit 2 and the borrow 1 from 8 in column 4 and get 5.
5 is the next digit of our result.

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 6 in column 5 and get 5.
5 is the next digit of our result.

So, 68626 - 12629 = 55997.