Alright, let's solve this problem step by step. We have 4108 and 5288 and we're adding them together.

Step 1: We'll start by adding the digits 8 & 8 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 8 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 2 in column 3 and get 3.

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

So, 4108 + 5288 = 9396.

