Okay, let's tackle this math problem. We're starting with 48083 and subtracting 42077.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 3 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 8 in column 2 and get 0.
0 is the next digit of our result.

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

Step 4: We'll start by subtracting the digit 2 and the borrow 0 from 8 in column 4 and get 6.
6 is the next digit of our result.

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

So, 48083 - 42077 = 6006.