Okay, we are tasked with adding 7586 and 1417. Let's begin!

Step 1: We'll start by adding the digits 6 & 7 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 8 & 1 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 5 & 4 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 1 in column 4 and get 9.

So, 7586 + 1417 = 9003.

