1. **Problem:** Find the value of $a$ such that the lines $L_1: 3x - ay - 2 = 0$ and $L_2: 6x - 4y + 3 = 0$ are parallel. 2. **Formula and rule:** Two lines $Ax + By + C = 0$ and $Dx + Ey + F = 0$ are parallel if their slopes are equal. The slope of a line $Ax + By + C = 0$ is $-\frac{A}{B}$. 3. **Calculate slopes:** - Slope of $L_1$ is $-\frac{3}{-a} = \frac{3}{a}$. - Slope of $L_2$ is $-\frac{6}{-4} = \frac{6}{4} = \frac{3}{2}$. 4. **Set slopes equal:** $$\frac{3}{a} = \frac{3}{2}$$ 5. **Solve for $a$:** Multiply both sides by $a$ and then by 2: $$3 \times 2 = 3 \times a$$ $$6 = 3a$$ Divide both sides by 3: $$a = 2$$ 6. **Answer:** The value of $a$ is $2$. **Final answer:** C. 2