The axis of symmetry of a parabola in the form
[tex]y=ax^2+bx+c[/tex]
is a vertical line
[tex]x=k[/tex]
where k is the x coordinate of the vertex of the parabola.
The x coordinate of the vertex of the parabola is given by
[tex]-\dfrac{b}{2a}[/tex]
which in your case is
[tex]-\dfrac{-6}{2\cdot \frac{1}{4}}=\dfrac{6}{\frac{1}{2}}=6\cdot 2=12[/tex]
So, the axis of symmetry is the line x=12.