Let's solve this addition problem. We have 1029 and 8165, and we need to add them together.

Step 1: We'll start by adding the digits 9 & 5 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 2 & 6 in column 2 and get 9.

Step 3: We'll start by adding the digits 0 & 1 in column 3 and get 1.

Step 4: We'll start by adding the digits 1 & 8 in column 4 and get 9.

So, 1029 + 8165 = 9194.

