Okay, we are given 8439 and 4401. Let's add them up step by step.

Step 1: We'll start by adding the digits 9 & 1 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 3 & 0 in column 2 and get 4.

Step 3: We'll start by adding the digits 4 & 4 in column 3 and get 8.

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

So, 8439 + 4401 = 12840.

