Okay, let's tackle this math problem. We're starting with 646138 and subtracting 88184.

Step 1: We'll start by subtracting the digit 4 and the borrow 0 from 8 in column 1 and get 4.
4 is the first digit of our result.

Step 2: We'll start by subtracting the digit 8 and the borrow 0 from 3 in column 2 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 3: We'll start by subtracting the digit 1 and the borrow 1 from 1 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 8 and the borrow 1 from 6 in column 4 and get -3.
We add -3 to 10 and get 7 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 6 in column 6 and get 5.
5 is the next digit of our result.

So, 646138 - 88184 = 557954.