A simple solution is to mount or secure it to a rigid board. Good backing options mentioned were matte board from a framing/craft shop, foam core, or a compressed cardboard/fiber board. For a 16×12 target, these are common sizes and easy to cut.

If you want to avoid a permanent mount, use a board cut to the target’s size and hold the target flat with photo corners, binder clips, or similar removable fasteners. That lets you flatten it for shooting without risking damage or making the setup irreversible.

If you do want a more finished support, a framing shop can usually supply matte board and mounting adhesive. But unless you’re sure you’ll never need to remove or replace the target, a non-permanent method is safer.

In short: use a rigid backing such as matte board or foam core, and prefer removable mounting unless you’re certain about a permanent bond.