Alright, let's solve this problem step by step. We have 4174 and 4034 and we're adding them together.

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

Step 2: We'll start by adding the digits 7 & 3 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 0 in column 3 and get 2.

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

So, 4174 + 4034 = 8208.

