We've got two numbers: 4586 and 5943. Let's find their sum.

Step 1: We'll start by adding the digits 6 & 3 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 4 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 5 & 9 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 4 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 4586 + 5943 = 10529.

