If you walk around while brushing your teeth, you'll end up stabbing yourself in the throat so be careful!
If you walk around while brushing your teeth, you might hurt your throat (with your toothbrush) so be careful!
「歯磨きしながら」= while brushing your teeth
「歩いたら」= if you walk (around)
「喉を突く」= you'll stab yourself in the throat / you'll hurt your throat (hurt=傷をつける、痛める)
「気をつける」= be careful
「歯磨きしながら歩いたら喉を突くから気を付けて」= If you walk around while brushing your teeth, you'll end up stabbing yourself in the throat so be careful! / If you walk around while brushing your teeth, you might hurt your throat (with your toothbrush) so be careful!