Let's break this down. We're going to add 1974 and 3365 together.

Step 1: We'll start by adding the digits 4 & 5 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 6 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

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

Step 4: We'll start by adding the digits 1 & 3 in column 4 and get 5.

So, 1974 + 3365 = 5339.

