Let's get this math done. We have 554550 and 66379, 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 0 in column 1 and get -9.
We add -9 to 10 and get 1 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 5 in column 2 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 3: We'll start by subtracting the digit 3 and the borrow 1 from 5 in column 3 and get 1.
1 is the next digit of our result.

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

Step 5: We'll start by subtracting the digit 6 and the borrow 1 from 5 in column 5 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 5 in column 6 and get 4.
4 is the next digit of our result.

So, 554550 - 66379 = 488171.