If you're just starting out with this type of problem, your best bet would be to multiply out the given equation and collect like terms, so as to rewrite it in the form y = ax^2 + bx + c.
Then the equation of the axis of symmetry would be x = -b/(2a).
Can you finish this problem?
Hint: y + 3x -6 = -3(x-2)^2 + 4 becomes y + 3x - 6 = -3(x^2 - 4x + 4) + 4,
or y + 3x - 6 = -3x^2 - 12x + 12 + 4