Okay, let's tackle this math problem. We're starting with 751527 and subtracting 63666.

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

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

Step 3: We'll start by subtracting the digit 6 and the borrow 1 from 5 in column 3 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

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

So, 751527 - 63666 = 687861.