Show[RegionPlot[x+y ≥ -6&&x+2*y ≥ -8,{x,-4,0},{y,-3,0},PlotLegends  ->"Expressions"],Plot[((-2)/3) *x-(14/3) ,{x,-4,0},PlotLegends -> "Expressions",PlotStyle -> {Red}],Plot[((-2)/3)* x-3,{x,-4,0},PlotLegends -> "Expressions",PlotStyle ->{Green}]]

(Legended[, ({{(LineLegend[-((2 x)/3)-(14/3)])}, {(SwatchLegend[x+y≥-6∧x+2 y≥-8])}, {(LineLegend[-((2 x)/3)-3])}})])