The intersection of two sets, written [tex]A\cap B[/tex] is the set that contains all elements in BOTH of the original sets.
In this case:
[tex]A\cap C=\{0,1,2,3\}\cap\{0,a,2,b\}=\{0,2\}[/tex]
Unless you are told somewhere else what a and b are equal to, none of the given choices is correct.
