Learn Finnish: Vihainen mies lyö ovea paljain nyrkein. - The angry man hits the door with bare fists.

The instructive case is formed by adding the suffix -n to the plural stem of the word. For nyrkki (fist), the plural stem is nyrkei-, making nyrkein. Crucially, any modifying adjective must also agree in the instructive case. So, the adjective paljas (bare) is also put into the instructive plural, becoming paljain.

Why does the stem of paljas change to paljai- before adding the instructive ending?

Words ending in -as or -äs have a basic stem ending in a long vowel (like paljaa-). When you form the plural stem, the plural -i- marker replaces the final vowel, resulting in paljai-. Adding the instructive -n gives you paljain.

Could I just use the adessive case (paljailla nyrkeillä) to mean "with bare fists"?

Grammatically, yes, the adessive case is the standard way to express the instrument of an action. However, the instructive case is heavily preferred in fixed expressions involving body parts used as tools (like paljain jaloin for "barefoot" or paljain silmin for "with the naked eye"). Using paljain nyrkein sounds much more natural and idiomatic in Finnish.

Why is the object ovea in the partitive case?

The verb lyödä (to hit) typically takes a partitive object. Hitting is usually an irresultative action, meaning it doesn't inherently reach a definitive endpoint or cause a total change of state. If he were to completely break the door, the object might take the accusative case, but the ongoing action of simply hitting it requires the partitive.