Plane = 3x-4y+6z-2==0;

Solve[Plane,z]

Plot3D[(1/6) (2-3 x+4 y),{x,-5,5},{y,-5,5}, AxesLabel->{"x","y","z"}]

Plot1=ContourPlot3D[Evaluate[Plane],{x,-5,5},{y,-5,5},{z,-5,5}]

LineEqn = {2t-1,6t+4,-t+2};

Plot2=ParametricPlot3D[LineEqn,{t,-3,3}]

Show[{Plot1,Plot2}, AxesLabel->{x,y,z}]

Plane

LineEqn

LineEqn[[3]]

Plane/.{x->LineEqn[[1]],y->LineEqn[[2]],z->LineEqn[[3]]}

Solve[%,t]

Solve[-2+6 (2-t)+3 (-1+2 t)-4 (4+6 t)==0,t]

LineEqn/.{t->-3/8}

Plot3=Graphics3D[{Green,Sphere[{-(7/4),(7/4),(19/8)},0.2]}];

Show[{Plot1,Plot2,Plot3}]