Alright, let's solve this problem step by step. We have 142629 and 88393, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 3 and the borrow 0 from 9 in column 1 and get 6.
6 is the first digit of our result.

Step 2: We'll start by subtracting the digit 9 and the borrow 0 from 2 in column 2 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

Step 3: We'll start by subtracting the digit 3 and the borrow 1 from 6 in column 3 and get 2.
2 is the next digit of our result.

Step 4: We'll start by subtracting the digit 8 and the borrow 0 from 2 in column 4 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

Step 5: We'll start by subtracting the digit 8 and the borrow 1 from 4 in column 5 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

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

So, 142629 - 88393 = 54236.