Hi Casimir,

Is this what you are trying to do? Yellow does not show well on a white background so I changed it to to Cyan

Show[
 {Plot[f[x], {x, -6, 15}, PlotStyle -> Blue, 
   PlotLegends -> LineLegend[{Blue}, {"\[ScriptCapitalU]"}]],
  Plot[g[x], {x, 0, 15}, PlotStyle -> Green, 
   PlotLegends -> LineLegend[{Green}, {"\[ScriptCapitalU]'"}]],
  Plot[a[x], {x, 0, 6}, PlotStyle -> Red, 
   PlotLegends -> LineLegend[{Red}, {"After Price\[DifferenceDelta]"}]],
  Plot[b[x], {x, 0, 2.667}, PlotStyle -> Red, 
   PlotLegends -> LineLegend[{Red}, {"Before Price\[DifferenceDelta]"}]],
  Plot[h[x], {x, 0, 4.1}, PlotStyle -> Cyan, 
   PlotLegends -> LineLegend[{Cyan}, {"Hypothetical Budget Line"}]],
  ListPlot[{{1.333, 3}, {2, 2}, {3, 3}} -> {"A", "B", "C"}]}, 
 PlotRange -> {{0, 10}, {0, 6.5}},
 GridLines -> Automatic,
 AxesOrigin -> {0, 0},
 FrameLabel -> {"Good x", "Good y"},
 Frame -> True,
 PlotLabel -> "Price of good y is cheaper", 
 LabelStyle -> {GrayLevel[0], Bold, Italic}
 ]