What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?

Convert to y=ax^2+bx+c form
y+3x-6=-3(x-2)^2+4
exponent
y+3x-6=-3(x^2-4x+4)+4
distribute
y+3x-6=-3x^2+12x-12+4
minus 3x both sides
y-6=-3x^2+9x-8
add 6 both sides
y=-3x^2+9x-2

in form ax^2+bx+c=y
x coordinate of the vertex=-b/2a
and the axis of symmetry is the x coordianat
a=-3
b=9
-9/(2*-3)=-9/-6=3/2

x=3/2 is axis of symmetry