Alright, let's solve this problem step by step. We have 1974 and 2835 and we're adding them 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 & 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 9 & 8 in column 3 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

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

So, 1974 + 2835 = 4809.

