To find the sum of $456$ and $789$, we can use the column addition method. This involves writing the numbers one below the other, ensuring that the digits are aligned by place value (units, tens, hundreds). Here’s how it looks:

We begin by adding the units column. Adding $6$ and $9$ gives us $15$. We write down the $5$ in the units place and carry over the $1$ to the tens column.

Next, we move to the tens column. We add $5$ and $8$, which equals $13$. Adding the $1$ we carried over results in $14$. We write down $4$ in the tens place and carry over another $1$ to the hundreds column.

Finally, we add the hundreds column. $4$ plus $7$ equals $11$, and adding the $1$ carried over brings us to $12$. We write down $2$ in the hundreds place and place the $1$ in the thousands place.

The completed addition looks like this:

Thus, the sum of $456$ and $789$ is $1,245$. This method is effective for accurately managing any carrying of values to the next column, making it a reliable technique for adding large numbers.