Okay, let's tackle this math problem. We're starting with 610075 and subtracting 96365.

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

Step 2: We'll start by subtracting the digit 6 and the borrow 0 from 7 in column 2 and get 1.
1 is the next digit of our result.

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

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

Step 5: We'll start by subtracting the digit 9 and the borrow 1 from 1 in column 5 and get -9.
We add -9 to 10 and get 1 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, 610075 - 96365 = 513710.