Try:
prmtrcplt1 =
ParametricPlot[
Evaluate@Table[{x, a Sin[2 x]}, {a, 0, 1, 1/4}], {x, -Pi, Pi},
PlotRange -> {{-Pi, Pi}, {-3, 3}}, ImageSize -> 300];
prmtrcplt2 =
ParametricPlot[
Evaluate@Table[{a Sin[2 x], x}, {a, 0, 1, 1/4}], {x, -Pi, Pi},
PlotRange -> {{-Pi, Pi}, {-3, 3}}, ImageSize -> 300];
Row[{prmtrcplt1, prmtrcplt2}, Spacer[5]]
Or:
prmtrcplt3[a_] :=
ParametricPlot[{x, a Sin[2 x]}, {x, -Pi, Pi},
PlotRange -> {{-Pi, Pi}, {-3, 3}}, ImageSize -> 300];
prmtrcplt4[a_] :=
ParametricPlot[{a Sin[2 x], x}, {x, -Pi, Pi},
PlotRange -> {{-Pi, Pi}, {-3, 3}}, ImageSize -> 300];
Row[{Table[prmtrcplt3[a], {a, 0, 1, 1/3}],
Table[prmtrcplt4[a], {a, 0, 1, 1/3}]}, Spacer[5]]