Attacks are always associated with a hand. This could be the hand that uses a weapon, that casts a spell, or that performs an unarmed strike. The first attack you make with a given hand has no penalty to hit. Each subsequent attack you make with that hand in the same turn incurs a cumulative -3 attack penalty to hit. Your attack penalty resets to 0 at the end of your turn.
Lord Goobelthorp is wielding a claymore in two hands. The first attack they make with the claymore has no penalty to hit. If they make a second attack with the claymore in the same turn, that attack incurs a -3 penalty to hit. If they make a third attack with the claymore in the same turn, that attack incurs a -6 penalty to hit.
Kaflimbo is wielding a shortsword in each hand. The first attack they make with one of the shortswords has no penalty to hit. If they make a second attack with their other shortsword in the same turn, that attack also has no penalty to hit. If they make a third attack with one of the shortswords in the same turn, that attack incurs a -3 penalty to hit.
Tizzy Snomblom has a war hammer in one hand and a tower shield in the other. The arm with the tower shield is also holding a dagger, although they cannot attack with it. The first attack they make with the hammer has no penalty to hit. If they make a second attack with the hammer in the same turn, that attack incurs a -3 penalty to hit. If they make a third attack with the hammer in the same turn, that attack incurs a -6 penalty to hit.
Flaxer Gogo has a longsword in one hand, a dagger in the other, and a buckler shield strapped to the arm with their dagger. The first attack they make with the longsword has no penalty to hit. Since they're using is buckler shield (and not some larger type of shield), they can also make a second attack with the dagger in the same turn without incurring a penalty to hit. If they make a third attack with the longsword or the dagger in the same turn, that attack incurs a -3 penalty to hit.