Solve for Intersections: Finding X in y = 2x(x - 6) with the X-Axis

To solve this problem, let's determine the points where the function $y = 2x(x-6)$ intersects the X-axis.

Step 1: Set the quadratic function equal to zero to find the roots, which represents the X-axis intersection points:
$2x(x-6) = 0$.

Step 2: Consider each factor of the product expression separately:
Set $2x = 0$ and solve for $x$:
$x = 0$

Step 3: Set the second factor equal to zero as well:
Set $x-6 = 0$ and solve for $x$:
$x = 6$

Step 4: These solutions give us the x-coordinates of the intersection points. Since we set $y=0$, the points of intersection are
$(0, 0)$ and $(6, 0)$.

Therefore, the function intersects the X-axis at the points $(0, 0)$ and $(6, 0)$.

This matches with the choice labeled as choice 2: $(6,0),(0,0)$.