\left \{ {{x+ \frac{y}{2} - \frac{x}{3} =4}|*6 \atop {x-\frac{y}{2}+\frac{y}{3}=-3}|*6} \right.
\left \{ {{6x+ 3y} -2x =24} \atop {6x-3y}+2y=-18} \right.
\left \{ {{4x+ 3y =24} \atop {6x-y=-18}|*3}} \right.
\left \{ {{4x+ 3y =24} \atop {18x-3y=-54}}} \right.
22x=-30
x=-\frac{15}{11}
x=-1\frac{4}{11}
4*(-\frac{15}{11})+3y=24
3y=24+\frac{60}{11}
3y=\frac{324}{11} |:3
y=\frac{108}{11}
y=9\frac{9}{11}