We have numbers 4261 and 8417. Let's start adding them together.

Step 1: We'll start by adding the digits 1 & 7 in column 1 and get 8.

Step 2: We'll start by adding the digits 6 & 1 in column 2 and get 7.

Step 3: We'll start by adding the digits 2 & 4 in column 3 and get 6.

Step 4: We'll start by adding the digits 4 & 8 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 4261 + 8417 = 12678.

