Solve Vertical Addition: 456 + 4 Step-by-Step

$\begin{aligned} &456 \\ +& \\ &~~~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}$$$

To solve this problem, we'll follow these steps:

• Step 1: Align the numbers vertically based on their place values:
  $456$
  + $004$
  $\underline{\phantom{457}}$

• Step 2: Start adding from the rightmost column (units place):
  6 (from 456) + 4 = 10.
  The result is 10, so we place 0 in the units place under the line, and carry over 1 to the next column (tens place).

• Step 3: Move to the tens place, including the carry over:
  5 (from 456) + 0 (from 004) + 1 (carry over) = 6.
  Place 6 in the tens place under the line.

• Step 4: Move to the hundreds place:
  4 (from 456) + 0 = 4.
  Place 4 in the hundreds place under the line.

The complete sum would look like this:
$456$
+ $004$
$\phantom{460} \underline{460}$

Therefore, the solution to the problem is $460$, which corresponds to choice 4.