$[(v_1,v_2),(v_3,v_4),(v_5,v_6),(v_7,v_8)] = [1,1,1,0]$

This particular case has $3$ assignments that’s why we multiplied by $3$,

(1). $[(v_1,v_2),(v_3,v_4),(v_5,v_6),(v_7,v_8)] = [(1,1),(1,1),(1,1),(0,0)]$

(2). $[(v_1,v_2),(v_3,v_4),(v_5,v_6),(v_7,v_8)] = [(1,1),(1,1),(1,1),(0,1)]$

(3). $[(v_1,v_2),(v_3,v_4),(v_5,v_6),(v_7,v_8)] = [(1,1),(1,1),(1,1),(1,0)]$