To check the validity of option B :-
Consider a graph $G$ with vertex set $V = \{1, 2, 3\}$ and edge between 1 & 2 is Red, 2 & 3 is Green & 1 & 3 is Red. Here vertex $3$ causes $G$ to violate the property given in the problem statement, but vertex 2 is not obeying option B.
To check the validity of option C:-
Let $V_R$ denotes the endpoint of a red colored edge, $V_B$ denotes endpoint of a blue colored edge and $V_G$ denotes the endpoint of a green colored edge
The given property $P4 in the problem statement can be expressed as
$\forall V [ V_R \Rightarrow V_B \vee \neg V_G]$
i.e., $\forall V [ \neg V_R \vee V_B \vee \neg V_G]$
If a graph $G$ does not satisfy the above property, then it becomes
$ \neg \forall V[\neg V_R \vee V_B \vee \neg V_G] = \exists V [V_R \wedge \neg V_B \wedge V_G]$
This is the statement in option C.
Since, option C implies option A
D is the correct option.