Let's break this down. We're going to add 5977 and 1108 together.

Step 1: We'll start by adding the digits 7 & 8 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 9 & 1 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 5 & 1 in column 4 and get 7.

So, 5977 + 1108 = 7085.

