Alright, let's solve this problem step by step. We have 1582 and 7041 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 1 in column 1 and get 3.

Step 2: We'll start by adding the digits 8 & 4 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 0 in column 3 and get 6.

Step 4: We'll start by adding the digits 1 & 7 in column 4 and get 8.

So, 1582 + 7041 = 8623.

