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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

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.”

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.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

Slinza's last ability triggers whenever any creature with power 4 or greater enters, not just one you control.

Slinza's first ability doesn't change the mana cost or mana value of any spell. It changes only the total cost you pay to cast Beast spells.

Any Beasts that enter at the same time as Slinza won't enter with an additional +1/+1 counter.

If one or more static abilities that apply to a creature entering change its power, those abilities are considered when determining whether Slinza's last ability triggers. The same is true for replacement effects that apply to it, such as entering with one or more +1/+1 counters (such as the effect of Slinza's second ability, not coincidentally) or entering as a copy of another creature.

Slinza's second ability applies to all Beasts creatures you control as they enter, even if they wouldn't ordinarily enter with any +1/+1 counters on them.

Slinza's first ability can't reduce the amount of colored mana you pay for a spell. It reduces only the generic mana component of that spell.

If Slinza enters at the same time as one or more other creatures with power 4 or greater, its last ability triggers once for each of those other creatures, plus one more time for itself.

You don't choose a target for Slinza's last ability at the time it triggers. Rather, a second "reflexive" ability triggers when you pay {1}{R}{G} this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.