Duergar Hedge-Mage

When Duergar Hedge-Mage enters, if you control two or more Mountains, you may destroy target artifact.
When Duergar Hedge-Mage enters, if you control two or more Plains, you may destroy target enchantment.

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March of the Machine Commander

When Duergar Hedge-Mage enters the battlefield, if you control two or more Mountains, you may destroy target artifact.
When Duergar Hedge-Mage enters the battlefield, if you control two or more Plains, you may destroy target enchantment.

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Both abilities are optional; you choose whether to use them when they resolve. If an ability has a target, you must choose a target even if you don't plan to use the ability.

Both abilities trigger at the same time. You can put them on the stack in any order.

Each of the triggered abilities has an "intervening 'if' clause." That means (1) the ability won't trigger at all unless you control two or more lands of the appropriate land type when the Hedge-Mage enters, and (2) the ability will do nothing if you don't control two or more lands of the appropriate land type by the time it resolves.

Each of the triggered abilities look at your lands individually. This means that if you only control two dual-lands of the appropriate types, both of the abilities will trigger.