We have numbers 3913 and 6637. Let's start adding them together.

Step 1: We'll start by adding the digits 3 & 7 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 3 in column 2 and get 5.

Step 3: We'll start by adding the digits 9 & 6 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 6 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 3913 + 6637 = 10550.

