chess online

why not queen to g6 or h5 ?

But from what I see, 2...Qg6 leaves black open to this:

1. ... Rxa4
2. Nd6 Qg6
3. Rf8+ Kh7
4. Ne8

Where black can't defend against 5. Nf6+. The best that can be hoped for is the queen sacrifices herself for the knight. Note that 3...Kxf8 is checkmate in short order:

3. Rf8+ Kxf8
4. Qd8+ Qe8
5. Qxe8#

And any attempt to save the queen is doomed:

4. Ne8 Qg5
5. Nf6+ Kg6
6. Qf7#

As for 2...Qh5, I can't see how black can hold after:

1. ... Rxa4
2. Nd6 Qh5
3. Rf8+ Kh7
4. Ne8 Qd1+
5. Kh2

Where white now threatens mate on g7. So black's best move is 4...Qxe8 (or 4...Qg6 transposing into the first line), once again sacrificing the queen. So it appears in both of these lines that white wins the queen for a knight, which is a worse proposition than the main line.