What month is the most unlucky is it February the 13th or June 13th?

It's June 13th, because Valentine's Day occurs just before February the 13th.

At least, that's what I think, but you could also argue the opposite point, that February 13th is more unlucky than June 13th, because it occurs just after Valentine's Day (assummed to be lucky), therefore it must be unlucky.

Hope this helps!