Can Nykthos be activated for its second ability, using the mana generated from the forest and wild growth?
I believe the answer is "no" as the cost must be payed before Nykthos can be tapped, and the mana from wild grown is only generated when Nykthos is tapped.
You don't get mana from Wild Growth until the land it is attached to activates and resolves its mana ability. This is a different moment from merely the tapping of that land.
106.11. To "tap [a permanent] for mana" is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, "Mana Abilities."
106.11a An ability that triggers whenever a permanent "is tapped for mana" or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.
If Wild Growth is enchanting Nykthos (which you didn't mention), then you can also be sure, that you cannot activate its ability until all its costs are paid. So therefore, you could not get to the point where Wild Growth will trigger unless you can come up with the prior.
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Nykthos, Shrine to Nyx & Wild Growth
Can Nykthos be activated for its second ability, using the mana generated from the forest and wild growth?
I believe the answer is "no" as the cost must be payed before Nykthos can be tapped, and the mana from wild grown is only generated when Nykthos is tapped.
106.11a An ability that triggers whenever a permanent "is tapped for mana" or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.
If Wild Growth is enchanting Nykthos (which you didn't mention), then you can also be sure, that you cannot activate its ability until all its costs are paid. So therefore, you could not get to the point where Wild Growth will trigger unless you can come up with the prior.
Awesome avatar provided by Krashbot @ [Epic Graphics].
Otherwise what you've said makes perfect sense, thank you.