Alright, let's solve this problem step by step. We have 8772 and 5874 and we're adding them together.

Step 1: We'll start by adding the digits 2 & 4 in column 1 and get 6.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 8 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 5 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 8772 + 5874 = 14646.

