Alright, let's solve this problem step by step. We have 6835 and 9031 and we're adding them together.

Step 1: We'll start by adding the digits 5 & 1 in column 1 and get 6.

Step 2: We'll start by adding the digits 3 & 3 in column 2 and get 6.

Step 3: We'll start by adding the digits 8 & 0 in column 3 and get 8.

Step 4: We'll start by adding the digits 6 & 9 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 6835 + 9031 = 15866.

