How do I remove a jammed game from my 3DS?

You’re an iFixit user. Grab your Phillips 0 screw driver and undo some thingamajigs in the shell. Take out the battery. Unscrew some more jiggers. You should be looking at a motherboard now if my memory serves right. From there, you will have more room to jimmy the game out of your 3DS. When that’s done, I strongly suggest you use your recovered game as a projectile to remind your brother of how much you love him.

An actual guide for getting to the motherboard - Nintendo 3DS Teardown