Alright, let's solve this problem step by step. We have 3999 and 5935 and we're adding them together.

Step 1: We'll start by adding the digits 9 & 5 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 3 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 & 9 in column 3 and get 19.
We'll write down the last digit 9 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 5 in column 4 and get 9.

So, 3999 + 5935 = 9934.

