If my opponent is paying for any card, and I will play [whi]Hate[/whi] in reaction what will hapend when my opponent then don't have enough resources to pay?

Triggering a Card Effect (v1.1)
In order to successfully trigger a card effect, the player must declare that he is activating the card, declare targets, then pay any additional costs denoted on
the card. If a player cannot fulfill any requirements to trigger a card effect, he cannot attempt to trigger it.

Hmm, I don't think the stack/chain quite works that way.

Your opponent pays the needed resources, and then reveals the card. Paying a cost is regarded as a part of playing the card. Thus there is no chance of playing actions between paying and playing the card.
After your opponent's unit has been paid, it is revealed from his hand and he decides where the unit goes. Playing a unit/support is regarded an action, so you DO have a chance to react to this unit hitting the desk. But do notice, your response can't do anything about the resources used to pay for this unit, as paying was a part of playing it (also note that units/supports don't stack/chain). Thus playing [whi]Hate[/whi] in that situation doesn't affect the unit. And it's the same thing even if your opponent played a tactic.

If you want to restrain your opponent from playing costly units, you need to play [whi]Hate[/whi] after your opponent's Kingdom phase or Quest phase.

Yep, what street said is correct. You can't "counter" a card with [whi]Hate[/whi]

That's why I don't play Hate...in my DE decks :)