Step 1: For two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be parallel :
$$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$
Step 2: Given line : $2x - 6y - 7 = 0$. Option (C) : $x - 3y - 7 = 0$.
Step 3: $$\frac{2}{1} = 2,\quad \frac{-6}{-3} = 2,\quad \frac{-7}{-7} = 1$$
Step 4: Since $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$, the lines are parallel.

Correct option : (C)