Let's break this down. We're going to add 1005 and 6966 together.

Step 1: We'll start by adding the digits 5 & 6 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 6 in column 2 and get 7.

Step 3: We'll start by adding the digits 0 & 9 in column 3 and get 9.

Step 4: We'll start by adding the digits 1 & 6 in column 4 and get 7.

So, 1005 + 6966 = 7971.

