Okay, we are given 581 and 7638. Let's add them up step by step.

Step 1: We'll start by adding the digits 1 & 8 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 3 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 0 & 7 in column 4 and get 8.

So, 581 + 7638 = 8219.

