Alright, let's solve this problem step by step. We have 9081 and 1896 and we're adding them together.

Step 1: We'll start by adding the digits 1 & 6 in column 1 and get 7.

Step 2: We'll start by adding the digits 8 & 9 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 8 in column 3 and get 9.

Step 4: We'll start by adding the digits 9 & 1 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 9081 + 1896 = 10977.

