Answer:
(6, 0, 0)
Explanation:
The x-intercept in this context is the point where the plane crosses the y-axis. The values of y and z are both zero there. Filling in those values, we get ...
x +2(0) +4(0) = 6
x = 6
The full set of coordinates for the point will be ...
(x, y, z) = (6, 0, 0)
_____
Additional comment
The equation of the plane in intercept form is ...
x/a +y/b +z/c = 1 . . . . . . . where a, b, c are the x-, y-, z-intercepts
Dividing the given equation by 6 will help you get this form.
x/6 +2y/6 +4z/6 = 1 ⇔ x/6 +y/3 +z/(3/2) = 1
The y-intercept is (0, 3, 0), and the z-intercept is (0, 0, 3/2).