Find the dissimilar pair of numbers from the choices below.

Let's check the equivalent values or operations for each pair:
* Option A: ${\left(\frac{3}{4}\right)}^3=\frac{27}{64}$.
* Option C: $\frac{8}{16}$ simplifies completely to $\frac{1}{2}$, and $\frac{2}{4}$ simplifies to $\frac{1}{2}$. They are equivalent fractions.
* Option D: $\frac{12}{30}$ simplifies completely to $\frac{2}{5}$ by dividing the numerator and denominator by $6$. They are equivalent fractions.

Looking closely at Option B:
$\frac{12}{28}$ simplifies completely to $\frac{3}{7}$ (dividing by $4$), which is not equivalent to $\frac{2}{3}$, nor does it follow a simple cubing relation like Option A. Thus, Option B is the odd one out.