The key move is
1. Ng5+!
Note that the knight can't be taken: 1... hxg5 loses to 2. Rh3+ Nh5 3. Rxh5#. So, Black has no choice but to retreat with
1... Kh8 2. Nxf7+ Kh7. At this point, it's tempting to play 3. Nxd8, after which White wins easily. But there is a move that's better still...
Instead of taking the queen, White plays
3. Qg5!!, threatening 4. Qg6#. Once again, the queen can't be taken: 3... hxg5 loses to 4. Rh3+ Nh5 5. Rxh5# (as before) - and 3... g6 loses immediately to 4. Qxh6#. Black's best hope is
3... Bxf5, after which White mates with
4. exf5! hxg5 5. Rh3+ Nh5 6. Rxh5#.
If you solved this, then you're better than me: I saw that 1. Ng5+ would win Black's queen, but then didn't see the queen sacrifice and the mate that followed
.