Okay, we are tasked with adding 9161 and 8953. Let's begin!

Step 1: We'll start by adding the digits 1 & 3 in column 1 and get 4.

Step 2: We'll start by adding the digits 6 & 5 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 9 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 9 & 8 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9161 + 8953 = 18114.

