$\left \{ {{x-y=8} \atop {3x+2y=4}} \right.$
⇔ $\left \{ {{2x-2y=16} \atop {3x+2y=4}} \right.$
⇔ $\left \{ {{5x=20} \atop {x-y=8}} \right.$
⇔ $\left \{ {{x=4} \atop {4-y=8}} \right.$
⇔ $\left \{ {{x=4} \atop {y=-4}} \right.$
Vậy HPT đã cho có nghiệm là: $\left \{ {{x=4} \atop {y=-4}} \right.$