To factor this quadratic function, there are many ways that you can do this, the most common approach used to graph anything would be to make a table of values. Basically, make a chart with x coordinates on one side and y coordinates on the other side. Pick any values for your x coordinates and then find the correct y coordinate that results when you place that specific x coordinate into the function. After getting many points, plot those points on the grid and it should give you a parabola.
Another way to graph the function is to find the x intercepts, you can do this by setting the function to zero, and factoring the trinomial, using the appropriate method, then find the x intercepts
y = 2x^2 - 8x + 6
0 = (2x^2 - 6x - 2x + 6)
0 = 2x(x - 3) - 2(x - 3)
0 = (2x - 2)(x - 3).