The intercepts are the points where the plane intersects the x, y, and z axes.
To find the x-intercept, we set y and z to zero in the equation and solve for x.
\[4x + 2(0) + 6(0) = 12\]
\[4x = 12\]
\[x = 3\]
So, the x-intercept is (3,0,0).
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