Step 1 :The given equation is in the form of a linear equation. To find out which points satisfy this equation, we can substitute the x and y coordinates of each point into the equation. If the equation holds true, then the point is a solution to the equation.
Step 2 :Let's consider the points (4, 0), (6, -3), (9, -1), (-2, -4), (7, 2), (0, 6).
Step 3 :Substituting these points into the equation, we find that the points (4, 0), (6, -3), (0, 6) satisfy the equation.
Step 4 :Final Answer: The points that are solutions to the equation \(3 x+2 y=12\) are \(\boxed{(4, 0), (6, -3), (0, 6)}\).