$\mathbf{\underline{Answer:\Rightarrow C}}$
$\mathbf{\underline{Explanation:\Rightarrow}}$
If $\mathbf{X = 0}$, then no cars arrive and the number of cars that do not get service $\mathbf{ = 0}$
If $\mathbf{X = 1}$, then no cars arrive and the number of cars that do not get service $\mathbf{ = 0}$
If $\mathbf{X = 2}$, then no cars arrive and the number of cars that do not get service $ \mathbf{ = 0}$
If $\mathbf{X = 3}$, then no cars arrive and the number of cars that do not get service $\mathbf{ = 0}$
If $\mathbf{X = 4}$, then no cars arrive and the number of cars that do not get service $ \mathbf{ = 0}$
If $\mathbf{X = 5}$, then no cars arrive and the number of cars that do not get service $ \mathbf{ = 1}$
If $\mathbf{X = 6}$, then no cars arrive and the number of cars that do not get service $ \mathbf{ = 2}$
$\mathbf{\vdots} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \vdots\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathbf{\vdots}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \vdots\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \vdots$
$\therefore \text{The expected number of cars missing out on service} \\\\= \sum(\text{number of cars that miss out being serviced})(\text{probability of this happening}) \\\\=\mathbf{ 0P(X = 0) + 0P(X = 1) + 0P(X = 2)+\cdots+1P(X = 5) + 2P(X = 6)+\cdots\cdots\cdots}$
So, the above expression can be represented in the compact form as:
$$\sum(\text{The number of cars that miss-out being serviced})(\text{Probabibility of this happening}) = \mathbf{\sum_{0}^{\infty}iP(X = i+4)}$$
$\therefore$ Option $\mathbf C$ is the right answer.