user8209: I have watched this video, where Kasparov explains the variations after his knight sacrifice. However, the position he analyses starting from 3:08, I think I am missing something.
Kasparov vs Karpov, 1990 World Finals
[FEN "r3qb1k/1b4p1/p2pr2p/3n4/Pnp1N1N1/6RP/1B3PP1/1B1QR1K1 w - - 0 1"]

1. Nxh6 Rxh6 2. Nxd6 Qxe1+ 3. Qxe1 Rxd6 4. Qe4 Nd3

What if black plays 
[FEN "r4b1k/1b4p1/p2r4/3n4/Pnp1Q3/6RP/1B3PP1/1B4K1 b - - 0 1"]

1... Nf6

instead of Nd3? Can't he both attack queen and defend h7 square? His chances of survival is so low, obviously, but I think Nf6 is better than Nd3, and worth analyzing.

user4444: Well, for one thing, Nf6 leaves the bishop on b7 hanging, and upon taking it, the queen will be attacking both the rook on a8 and the knight on b4.

user1099: Nf6 is followed by e.g.:
[FEN "r4b1k/1b4p1/p2r1n2/8/Pnp1Q3/6RP/1B3PP1/1B4K1 w - - 0 1"]

1. Qh4+ Kg8 2. Bxf6 Rxf6 3. Qxf6

with not only huge material advantage for white, but also some very nasty threats that are ultimately not defendable. So in short, there is not much to gain with Nf6.

8209: <p>I have watched <a href="https://www.youtube.com/watch?v=SMe-hvCwTRo" rel="nofollow">this</a> video, where Kasparov explains the variations after his knight sacrifice. However, the position he analyses starting from 3:08, I think I am missing something.</p>

<p><strong>Kasparov vs Karpov, 1990 World Finals</strong></p>

<pre><code>[FEN "r3qb1k/1b4p1/p2pr2p/3n4/Pnp1N1N1/6RP/1B3PP1/1B1QR1K1 w - - 0 1"]

1. Nxh6 Rxh6 2. Nxd6 Qxe1+ 3. Qxe1 Rxd6 4. Qe4 Nd3
</code></pre>

<p>What if black plays </p>

<pre><code>[FEN "r4b1k/1b4p1/p2r4/3n4/Pnp1Q3/6RP/1B3PP1/1B4K1 b - - 0 1"]

1... Nf6
</code></pre>

<p>instead of Nd3? Can't he both attack queen and defend h7 square? His chances of survival is so low, obviously, but I think Nf6 is better than Nd3, and worth analyzing.</p>
 4444: <p>Well, for one thing, Nf6 leaves the bishop on b7 hanging, and upon taking it, the queen will be attacking both the rook on a8 and the knight on b4.</p>
 1099: <p>Nf6 is followed by e.g.:</p>

<pre><code>[FEN "r4b1k/1b4p1/p2r1n2/8/Pnp1Q3/6RP/1B3PP1/1B4K1 w - - 0 1"]

1. Qh4+ Kg8 2. Bxf6 Rxf6 3. Qxf6
</code></pre>

<p>with not only huge material advantage for white, but also some very nasty threats that are ultimately not defendable. So in short, there is not much to gain with Nf6.</p>
