Let's break this down. We're going to add 6443 and 1278 together.

Step 1: We'll start by adding the digits 3 & 8 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 4 & 7 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 2 in column 3 and get 7.

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

So, 6443 + 1278 = 7721.

