Alright, let's solve this problem step by step. We have 1461 and 8630 and we're adding them together.

Step 1: We'll start by adding the digits 1 & 0 in column 1 and get 1.

Step 2: We'll start by adding the digits 6 & 3 in column 2 and get 9.

Step 3: We'll start by adding the digits 4 & 6 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 8 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 1461 + 8630 = 10091.

