Question: How does the stack work for this scenario?

[Hushwing Gryff](http://gatherer.wizards.com/Pages/Search/Default.aspx?name=%2b%5bHushwing%20Gryff%5d) is already in play and the player goes to cast [Eater of Days](http://gatherer.wizards.com/Pages/Search/Default.aspx?name=%2b%5bEater%20of%20Days%5d) so the Hushwing Gryff will cancel out the loss of two turns. In response the opponent either casts [Lightning Bolt](http://gatherer.wizards.com/Pages/Search/Default.aspx?name=%2b%5bLightning%20Bolt%5d) or [Path to Exile](http://gatherer.wizards.com/Pages/Search/Default.aspx?name=%2b%5bPath%20to%20Exile%5d) on the Hushwing Gryff while Eater of Days is still on the stack. 

Does either the Bolt or Path remove the Hushwing Gryff, so when the Eater of Days resolves the player loses two turns?

Answer: 
The opponent can use either spell to target [Hushwing Gryff](http://gatherer.wizards.com/Pages/Search/Default.aspx?name=%2b%5bHushwing%20Gryff%5d) while Eater of Days is on the stack. In this case,

* The spell resolves first, removing Hushwing Gryff from the battlefield.
* Eater of Days resolves, and as there is no Hushwing Gryff on the battlefield the caster of Eater of Days loses two turns.
Yes, that's how it works. Basically, what is cast *last* will resolve *first*. Once the Eater of Days enters the battlefield, Hushwing Gryff is already gone and the enter-the-battlefield trigger will function as normal.