\[\dfrac{8}{6} - \dfrac{5}{4} = {}\]
To subtract fractions, we need to find a common denominator. The least common multiple of 6 and 4 is 12, so let's write both fractions with a denominator of 12.
For $\dfrac{8}{6}$, we multiply the numerator and denominator by 2 to get $\dfrac{16}{12}$.
For $\dfrac{5}{4}$, we multiply the numerator and denominator by 3 to get $\dfrac{15}{12}$.
Now we can subtract the fractions:
\[\dfrac{16}{12} - \dfrac{15}{12} = \dfrac{16-15}{12} = \dfrac{1}{12}.\]
So, $\dfrac{8}{6} - \dfrac{5}{4} = \boxed{\dfrac{1}{12}}$.