Alright, let's solve this problem step by step. We have 4897 and 1688 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 8 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 8 in column 2 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 8 & 6 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 4 & 1 in column 4 and get 6.

So, 4897 + 1688 = 6585.

