We need to complete the square here, i hope that's what you did. perhaps you're not comfortable with it? if you have any questions, just ask away. anyway, here goes

3x^2 + 12x + 7 = 3(x^2 + 4x) + 7

......................= 3(x^2 + 4x + (2)^2 - (2)^2) + 7

......................= 3[(x + 2)^2 - 4] + 7

......................= 3(x + 2)^2 - 12 + 7

......................= 3(x + 2)^2 - 5

(ii) Hence write down the equation of the line of symmetry of the curve y=3x²+12x+7

Now a parabola is symmetric about it's vertex. and when a parabola is written in the form:

y = a(x - h)^2 + k

then the vertex is given by (h,k)

we have 3(x + 2)^2 - 5 so our vertex is at (-2,-5)

since this is a parabola with a vertical axis (opens up or down, in this case up) the line of symmetry is just x = -2