Solve the Problem $c$ Are All Multiples of Two and Are All Less Than

Multiple Choice

Solve the problem.
-A certain part of a metropolitan area has a palindromic, 5-digit area code, say abcde, satisfying these conditions:
a, b and $c$ are all multiples of two and are all less than 8 ;
$a \neq b$ but $a + b = 6$ ;
$c \neq d$ but $a + c = 12$ ;
$\mathrm { e } \neq \mathrm { b }$ or $\mathrm { d }$ ;
$b + d \neq 4$ .
Determine the area code.

A) 60606
B) 44244
C) 24842
D) 42024