Alright, let's solve this problem step by step. We have 3972 and 4561 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 7 & 6 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 5 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 4 in column 4 and get 8.

So, 3972 + 4561 = 8533.

