Alright, let's solve this problem step by step. We have 8779 and 1004 and we're adding them together.

Step 1: We'll start by adding the digits 9 & 4 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 7 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 8 & 1 in column 4 and get 9.

So, 8779 + 1004 = 9783.

