Not to worry, we've got 4004 and 8635. Let's get to adding them!

Step 1: We'll start by adding the digits 4 & 5 in column 1 and get 9.

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

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

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

So, 4004 + 8635 = 12639.

