Alright, let's solve this problem step by step. We have 3582 and 9377 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 7 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 7 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 3 in column 3 and get 9.

Step 4: We'll start by adding the digits 3 & 9 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 3582 + 9377 = 12959.

