Alright, let's solve this problem step by step. We have 8823 and 8791 and we're adding them together.

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

Step 2: We'll start by adding the digits 2 & 9 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 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 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8823 + 8791 = 17614.

