Let's break this down. We're going to add 6568 and 1903 together.

Step 1: We'll start by adding the digits 8 & 3 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 6 & 0 in column 2 and get 7.

Step 3: We'll start by adding the digits 5 & 9 in column 3 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 1 in column 4 and get 8.

So, 6568 + 1903 = 8471.

