Answer
$(6,0,0)$.
Work Step by Step
To know where the plane
$$ -2x - 3y + 4z = 12$$
intersects x-axis, we put $y=z=0$ and find the vale of $x$ that is
$$ -2x=12 \Longrightarrow 3=6$$
hence the plane intersects x-axis at the point $(6,0,0)$.