user3630: What's black's best possible move and why?
[Title "Black to move"]
[StartFlipped "0"]
[fen "r3k3/pp2b3/1qn1Np2/2p1p2Q/4P2p/1NP4P/PP3Pr1/2KR4 b - - 0 1"]


user2042: 
What's black's best possible move and why?

Unfortunately, Black will lose this game. His king is indeed in check, but he can postpone mate only with 1...Rg6. The problem with Black's position is that king has no viable retreat: 

He can't go to d-file as he would be in check from rook on d1;
He can't go to f8 because he would be in check from knight on e6;
He can't go to e7 as Black bishop stands there;
He can't go to f7 because White queen controls that square so he would be again in check;

After 1...Rg6 White plays Qxg6 and gives checkmate:
[Title "White mates after Rg6"]
[StartFlipped "0"]
[fen "r3k3/pp2b3/1qn1Np2/2p1p2Q/4P2p/1NP4P/PP3Pr1/2KR4 b - - 0 1"] 

1...Rg6 2.Qg6# 1-0


3630: <p>What's black's best possible move and why?</p>

<pre><code>[Title "Black to move"]
[StartFlipped "0"]
[fen "r3k3/pp2b3/1qn1Np2/2p1p2Q/4P2p/1NP4P/PP3Pr1/2KR4 b - - 0 1"]
</code></pre>
 2042: <blockquote>
  <p>What's black's best possible move and why?</p>
</blockquote>

<p>Unfortunately, Black will lose this game. His king is indeed in check, but he can postpone mate only with <code>1...Rg6</code>. The problem with Black's position is that king has no viable retreat: </p>

<ol>
<li>He can't go to <code>d-file</code> as he would be in check from rook on <code>d1</code>;</li>
<li>He can't go to <code>f8</code> because he would be in check from knight on <code>e6</code>;</li>
<li>He can't go to <code>e7</code> as Black bishop stands there;</li>
<li>He can't go to <code>f7</code> because White queen controls that square so he would be again in check;</li>
</ol>

<p>After <code>1...Rg6</code> White plays <code>Qxg6</code> and gives checkmate:</p>

<pre><code>[Title "White mates after Rg6"]
[StartFlipped "0"]
[fen "r3k3/pp2b3/1qn1Np2/2p1p2Q/4P2p/1NP4P/PP3Pr1/2KR4 b - - 0 1"] 

1...Rg6 2.Qg6# 1-0
</code></pre>
