As has been said in the comments to your question, because all plotting functions are based on strictly numerical calculations, you must give definite values to all six parameters. If you are in the position where you have no good idea how function behaves as the parameters vary, you can explore the situation with Manipulate. Here is an example.

f[α_, β_, γ_, δ_, p_, q_][x_, y_] := (x y)^(p - 1)/(α + β x + γ y + δ x y)^(p + q) With[{ϵ = .0001}, Manipulate[ ContourPlot[f[α, β, γ, δ, p, q][x, y], {x, 0, 2}, {y, 0, 2}], {α, ϵ, 1, Appearance -> "Labeled"}, {β, ϵ, 1, Appearance -> "Labeled"}, {γ, ϵ, 1, Appearance -> "Labeled"}, {δ, ϵ, 1, Appearance -> "Labeled"}, {p, 1, 4, 1, Appearance -> "Labeled"}, {q, 1, 4, 1, Appearance -> "Labeled"}]] 

Note: I have no clue about what comprise good ranges for either the parameters or the variables. I made some simple assumption about them. You should revise these assumptions to suit your needs.

As has been said in the comments to your question, because all plotting functions are based on strictly numerical calculations, you must give definite values to all six parameters. If you are in the position where you have no good idea how the function behaves as the parameters vary, you can explore the situation with Manipulate. Here is an example.

f[α_, β_, γ_, δ_, p_, q_][x_, y_] := (x y)^(p - 1)/(α + β x + γ y + δ x y)^(p + q) With[{ϵ = .0001}, Manipulate[ ContourPlot[f[α, β, γ, δ, p, q][x, y], {x, 0, 2}, {y, 0, 2}], {α, ϵ, 1, Appearance -> "Labeled"}, {β, ϵ, 1, Appearance -> "Labeled"}, {γ, ϵ, 1, Appearance -> "Labeled"}, {δ, ϵ, 1, Appearance -> "Labeled"}, {p, 1, 4, 1, Appearance -> "Labeled"}, {q, 1, 4, 1, Appearance -> "Labeled"}]] 

Note: I have no clue about what comprise good ranges for either the parameters or the variables. I made some simple assumptions about them. You should revise these assumptions to suit your needs.