Example 3 In the expression
$$
|x+1|+|x+2|+|x+3|+|x+4|
$$

by substituting different values of $x$, we get corresponding values. Among these corresponding values, the minimum value is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
Explanation: The original problem can be transformed into: On the number line, there are four points $A, B, C, D$, with their corresponding values being $-1, -2, -3, -4$. Find a point $P$ such that $PA + PB + PC + PD$ is minimized (as shown in Figure 3).

When point $P$ is on the segment $AD$, $PA + PD$ achieves the minimum value of 3; when point $P$ is on the segment $BC$, $PB + PC$ achieves the minimum value of 1.
Therefore, the minimum value of $PA + PB + PC + PD$ is 4.
Hence, the answer is (D).