Okay, we are tasked with adding 2025 and 6564. Let's begin!

Step 1: We'll start by adding the digits 5 & 4 in column 1 and get 9.

Step 2: We'll start by adding the digits 2 & 6 in column 2 and get 8.

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

Step 4: We'll start by adding the digits 2 & 6 in column 4 and get 8.

So, 2025 + 6564 = 8589.

