Okay, we are tasked with adding 9176 and 2345. Let's begin!

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

Step 2: We'll start by adding the digits 7 & 4 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 1 & 3 in column 3 and get 5.

Step 4: We'll start by adding the digits 9 & 2 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 9176 + 2345 = 11521.

