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(The complete setup for this game can be found here: lsat/viewtopic.php?t=13729)
The correct answer choice is (B)
From the basic physical constraints of the game, Philadelphia can only connect with four other cities: Honolulu, Montreal, Toronto, and Vancouver. From the fourth rule, we know that Philadelphia cannot connect to both Toronto and Vancouver, and thus, the options for Philadelphia are H, M, and V/T. The question stem in #12 indicates that exactly three cities are connected with Philadelphia. Hence, we know we are selecting from the group of H, M, and V/T. But, because of the action of the third rule, when Philadelphia is connected with Honolulu, then Philadelphia must also be connected with Toronto. We can then determine in question #12 that Philadelphia is connected only to H, M, and T, as follows:
Because P cannot connect with V, we can eliminate answer choice (E). Also, because M is now connected to P, from the second rule we know that M cannot connect with any other city. Thus, answer choices (A), (C), and (D) can be eliminated. Therefore, answer choice (B) is proven correct by process of elimination.