Method 1 (brute force) :-
Method 2 :-
We know that,
sum of degree of vertices = 2 * number of edges (handshaking theorem)
$\implies 4+4+4+4+4+4 = 2 * e$
$\implies e = 12$
Also according to Euler's formula,
$r=e-v+2$
$\implies r= 12 -6 +2 $
$\implies r= 12 -6 +2 $
$\implies r= 8$
$\therefore$ Option $2.$ is correct.