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OK ... then let's check your variation ... :)

  1. Bxh6 gxh6
  2. Bxe4 dxe4
  3. Rg3+ Kh7
  4. Qh5 what about 4. ... Qe8?

5.. Ng5+!
Black is lost if he takes on g5 with the bishop or moves the king.
For example,
5.. Ng5+ Kg7
6.. Nxf7+ Kf6
7.. Qg6#
or
6.. ... Kh7 (or Kh8)
7.. Qxh6#
or
6.. ... Bg5
7.. Qxh6+ Kxf7
8.. Qh7+ Kf6
9.. fxg5#

In the other hand,
5.. Ng5+ Bxg5
6.. fxg5 Black is lost with any play

  1. Bxh6 gxh6
  2. Bxe4 dxe4
  3. Rg3+ Kh7
  4. Qh5 Qe8
  5. Ng5+ Bxg5
  6. fxg5 Rh8

What now?

7.. Qxh6 Kg8
8.. Rh3 and the mate is unstoppable

8. Rh3 Rxh6 and black wins! :)