Okay, we are tasked with adding 8129 and 7640. Let's begin!

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

Step 2: We'll start by adding the digits 2 & 4 in column 2 and get 6.

Step 3: We'll start by adding the digits 1 & 6 in column 3 and get 7.

Step 4: We'll start by adding the digits 8 & 7 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 8129 + 7640 = 15769.

