Let's get this math done. We have 6376 and 688, and we're going to subtract the second number from the first.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 6 in column 1 and get -2.
We add -2 to 10 and get 8 as the first digit of the result.

Step 2: We'll start by subtracting the digit 8 and the borrow 1 from 7 in column 2 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

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

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

So, 6376 - 688 = 5688.