Alright, let's solve this problem step by step. We have 4141 and 4674 and we're adding them together.

Step 1: We'll start by adding the digits 1 & 4 in column 1 and get 5.

Step 2: We'll start by adding the digits 4 & 7 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 1 & 6 in column 3 and get 8.

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

So, 4141 + 4674 = 8815.

