We have numbers 6305 and 7578. Let's start adding them together.

Step 1: We'll start by adding the digits 5 & 8 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 7 in column 2 and get 8.

Step 3: We'll start by adding the digits 3 & 5 in column 3 and get 8.

Step 4: We'll start by adding the digits 6 & 7 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 6305 + 7578 = 13883.

