Let's solve this addition problem. We have 8261 and 5863, and we need to add them together.

Step 1: We'll start by adding the digits 1 & 3 in column 1 and get 4.

Step 2: We'll start by adding the digits 6 & 6 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 2 & 8 in column 3 and get 11.
We'll write down the last digit 1 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, 8261 + 5863 = 14124.

