Alright, let's solve this problem step by step. We have 4035 and 4294 and we're adding them together.

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

Step 2: We'll start by adding the digits 3 & 9 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 2 in column 3 and get 3.

Step 4: We'll start by adding the digits 4 & 4 in column 4 and get 8.

So, 4035 + 4294 = 8329.

