Alright, let's solve this problem step by step. We have 3177 and 3674 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 4 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 15.
We'll write down the last digit 5 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 3 & 3 in column 4 and get 6.

So, 3177 + 3674 = 6851.

