Alright, let's solve this problem step by step. We have 8872 and 9764 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 4 in column 1 and get 6.

Step 2: We'll start by adding the digits 7 & 6 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 8 & 7 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 9 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 8872 + 9764 = 18636.

