Tactics Question

I am reading "How to Beat Your Dad in Chess" by Murray Chandler (which is, by the way, one of the best mating pattern books out there).  

Example 6 has this position:

This position only required a single Rook sacrifice on h8 for setting up checkmate.

Example 7 has this position:

This position required two Rook sacrifices on h8 to set up checkmate.

Both positions feature a fianchettoed Bishop.  What is the key difference between the positions that necessitate one sacrifice in the first and two sacrifices in the second.  I think it has something to do with the f6 Knight in the second position, but I am wondering if there is a larger point that I need to understand.

In the second position, are you sure 2 rook sacrifices are required? What I see is

1. Rh8+ Bxh8 2. Qh6 with mate following.

If you sacrifice both rooks, you wont have anything to support your queen in giving the checkmate.

Estragon your observation is good but I see it as having more to do with light squares and dark squares.  The first mate happens on light squares where f7 is blocked and mate is delivered on h7.  In the second mate, the mate happens on dark squares and the dark squared bishop must be eliminated.

#shady

1 Rh8 Bxh8  2 Qh6 can be defended by simply returning the Bishop to g6.  Then, if Qh7+, the King can escape via f8 to the Queenside.

In the first one, returning the Bishop to g6 would not work because mate is on h7.

So, I think, yes, ghostofmaroczy appears to be right.  The difference appears to lie in the square where my mating piece will be placed.

...but only as a pale, ethereal spectre.

#frombeyondthegrave