No problem, let's work through this together. We're starting with 61777 and are subtracting 50111 from it.

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

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

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

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

So, 61777 - 50111 = 11666.