Alright, let's solve this problem step by step. We have 4576 and 7642 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 2 in column 1 and get 8.

Step 2: We'll start by adding the digits 7 & 4 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 4 & 7 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 4576 + 7642 = 12218.

