Okay, we are tasked with adding 3634 and 2564. Let's begin!

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

Step 2: We'll start by adding the digits 3 & 6 in column 2 and get 9.

Step 3: We'll start by adding the digits 6 & 5 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 2 in column 4 and get 6.

So, 3634 + 2564 = 6198.

