Alright, let's solve this problem step by step. We have 6374 and 5204 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 & 0 in column 2 and get 7.

Step 3: We'll start by adding the digits 3 & 2 in column 3 and get 5.

Step 4: We'll start by adding the digits 6 & 5 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 6374 + 5204 = 11578.

