Your problem description describes a parallelogram shaped region of uniform probability in the x y plane, but your implementation is for a rectangular region. I think you want
Probability[
2 x + z == n, {x, z} \[Distributed]
ProductDistribution[DiscreteUniformDistribution[{-2, 4}],
DiscreteUniformDistribution[{-1, 1}]]];
DiscretePlot[%, {n, -6, 10}, ExtentSize -> 1/3]
