Alright, let's solve this problem step by step. We have 9819 and 8829 and we're adding them together.

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

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

Step 3: We'll start by adding the digits 8 & 8 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 9 & 8 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9819 + 8829 = 18648.

