QDoes this amulet's ability mean my leader can't take more than a total of 4 damage on the turn I activate it?

ANo. Any single instance of damage greater than 4 dealt to your leader that turn is reduced to 4.

For example, if your leader takes 5 damage twice, both instances are reduced to 4 for a total of 8 damage. If your leader takes 6 damage and then 3 damage, the first instance is reduced to 4 and the second is unaffected, giving a total of 7 damage.