so we have 6 teams of 3

a1, a2, a3
b1, b2, b3
...
f1, f2, f3

Team a
a1 cannot kiss a2, or a3 but can kiss everyone else, so 6*3 - 3 = 18-3=15
same with a2 and a3

so team a can kiss 15 ppl each so 15+15+15

Team b
cannot kiss other members of team b, and has already kissed team a so each member can only kiss 12 other people so 12+12+12

notice the pattern, each member of the team kisses the same number of ppl but with each passing team there are 3 less people....

15*3
12*3
9*3
6*3
3*3

once the last 2 teams have kissed each other the last team cannot kiss each other so we add up the above = 45*3 = 135

Don't forget that there are 2 kisses per cheek so 135*2 = 270 so B

hope that helps, it looks long above but it was short on paper

i tought it this way:

18 girls in total
any girl will kiss 15 different girls (since she won't kiss herself and the 2 girls from her team).
there are 18 girls in total so this will happen to all of them
18*15=270...

Shibal, though your soln gives you the right answer I don't think the method is right. First off you don't account for the number of kisses, had they kissed each other 3 times then your answer would be off though your method is the same. Also you don't account for 2 people kissing (however many kisses) more than once.

Though your method is quick and easy I don't think it would apply if the question was changed. Think you got lucky with the numbers.