Solution

We have,
$$9x+3y+12=0\quad ...(i)\\18x+6y+24=0\quad ...(ii)$$

Here,
$$a_1=9,b_1=3,c_1=12$$ and $$a_2=18,b_2=6,c_2=24$$
$$\dfrac{a_1}{a_2}=\dfrac{9}{18}=\dfrac{1}{2}; \quad \dfrac{b_1}{b_2} =\dfrac{3}{6}=\dfrac{1}{2}; \quad \dfrac{c_1}{c_2}=\dfrac{12}{24}=\dfrac{1}{2}$$
$$\Rightarrow \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$$
So equations (i) and (ii) represent coincident lines.