Alright, let's solve this problem step by step. We have 6372 and 2253 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 3 in column 1 and get 5.

Step 2: We'll start by adding the digits 7 & 5 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

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

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

So, 6372 + 2253 = 8625.

