The equation of a tangent to the parabola $y^2=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is:

The tangents to a parabola drawn from any point on its directrix are always perpendicular to each other.The given parabola is $y^2=8x$, which is of the form $y^2=4ax$ with $a=2$.The equation of the directrix is $x=-a⟹x=-2$.The point from which the perpendicular tangents are drawn must lie on the directrix $x=-2$.Since this point must also lie on the given tangent $y=x+2$:Substitute $x=-2$ into the equation:
$$y=-2+2=0$$
So, the point is $(-2,0)$.