It turns out to be a nice puzzle because it can be broken down into individual problems that can be independently analysed to arrive at a solution. The threat is black can aim all his big pieces down the f-h files in tandem with opening up the kings's safety - a standard hack attack.
SP076 Black to play - does black have a serious attack on white's king?
Answer bottom left hand corner of this page
Break the problem down into manageable chunks.
A) If ...f5 white plays e4 with a strong attack
B) if ...g5 white has the defense Bh4! followed by g3
C) if ...h5-h6 white has g3 stopping black's progress
A+B+C means white can safely proceed with a queen-side (c-side) attack