One fourth of a number exceeds one sixth of the number by $\dfrac{1}{2}$. The number is

1. 4
2. 6
3. 8
4. 12

Let the number be x.

One fourth of a number = $\dfrac{1}{4}x = \dfrac{x}{4}$

One sixth of the number = $\dfrac{1}{6}x = \dfrac{x}{6}$

According to the question, one fourth of a number exceeds one sixth of the number by $\dfrac{1}{2}$:

$\therefore \dfrac{x}{4} - \dfrac{x}{6} = \dfrac{1}{2} \\[1em] \Rightarrow \dfrac{3x - 2x}{12} = \dfrac{1}{2} \\[1em] \Rightarrow x = \dfrac{1}{2} \times 12 \\[1em] \Rightarrow x = \dfrac{1}{1} \times 6 \\[1em] \Rightarrow x = 6$

Hence, option 2 is the correct option.