Okay, we are tasked with adding 3439 and 8736. Let's begin!

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

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

Step 3: We'll start by adding the digits 4 & 7 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 8 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 3439 + 8736 = 12175.

