Alright, let's solve this problem step by step. We have 1902 and 6599 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 9 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 0 & 9 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 5 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 6 in column 4 and get 8.

So, 1902 + 6599 = 8501.

