Alternative rephrasing: $4000 dollars is given to your choice of either one of the top-rated charities for saving lives, or one of the top-rated charities for distributing birth control (or something else that reduces population growth).

That means a pure reduction on both sides in number of people on the planet, and- assuming there are currently too many people on the planet- a net reduction in suffering in the long run as there are fewer people to compete with each other, plus the good it does in the short run to women who don't have to go through unwanted pregnancies and raising the children and all the benefits associated with that (like being able to devote more resources to their other children, or possibly pursuing careers further, or the like).