The intersection point of a line crossing a surface is not displayed correctly In 3D Graphics

Use the "BSPTree" rendering method as this doesn't suffer from z-buffer precision issues and produces crisp edges:

theplot = 
  Show[{ParametricPlot3D[{x, y, 0}, {x, -4, 4}, {y, -4, 4}, 
     PlotStyle -> LightGray, Mesh -> None], 
    ParametricPlot3D[{0, 0, t}, {t, -8, 8}, PlotStyle -> Blue], 
    ParametricPlot3D[{x, 0, z}, {x, -3, 3}, {z, -3, 3}, 
     Mesh -> None]}];

GraphicsRow[{
  theplot
  , Style[theplot, RenderingOptions -> {"3DRenderingMethod" -> "BSPTree"}]
}]

Notice how the blue line juts out over the plane by a tiny fraction on the left image, but the right image renders correctly and uses BSP trees for visibility testing instead of a z-buffer.

It's a matter of viewpoint. I am using Windows 10 and MMA 12.0 and most other viewpoints had rendering looking a bit more precise.

I also changed the order of the three graphics, but the rendering stayed the same as yours.

c = ParametricPlot3D[{x, y, 0}, {x, -4, 4}, {y, -4, 4}, 
PlotStyle -> LightGray, Mesh -> None];
d = ParametricPlot3D[{0, 0, t}, {t, -8, 8}, PlotStyle -> Blue];
e = ParametricPlot3D[{a, 0, b}, {a, -3, 3}, {b, -3, 3}, Mesh -> None];
Show /@ Permutations[{c, d, e}]

We probably should have wrapped these in Module as part of best practices, especially since x and y show up in several places.