We can solve this together! We're beginning with 763707 and removing 6042 from it.

Step 1: We'll start by subtracting the digit 2 and the borrow 0 from 7 in column 1 and get 5.
5 is the first digit of our result.

Step 2: We'll start by subtracting the digit 4 and the borrow 0 from 0 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 0 and the borrow 1 from 7 in column 3 and get 6.
6 is the next digit of our result.

Step 4: We'll start by subtracting the digit 6 and the borrow 0 from 3 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 0 and the borrow 1 from 6 in column 5 and get 5.
5 is the next digit of our result.

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

So, 763707 - 6042 = 757665.