Okay, we are tasked with adding 8045 and 4645. Let's begin!

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

Step 2: We'll start by adding the digits 4 & 4 in column 2 and get 9.

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

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

So, 8045 + 4645 = 12690.

