\[\dfrac{8}{3} - \dfrac{2}{8} = {}\]
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 8 is 24.
So we can rewrite the fractions with this common denominator:
\[\dfrac{8}{3} - \dfrac{2}{8} = \dfrac{8 \cdot 8}{3 \cdot 8} - \dfrac{2 \cdot 3}{8 \cdot 3} = \dfrac{64}{24} - \dfrac{6}{24}.\]
Now that they have the same denominator, we can combine them:
\[\dfrac{64}{24} - \dfrac{6}{24} = \dfrac{64 - 6}{24} = \dfrac{58}{24}.\]
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
\[\dfrac{58}{24} = \dfrac{29 \cdot 2}{12 \cdot 2} = \dfrac{29}{12}.\]
So \[\dfrac{8}{3} - \dfrac{2}{8} = \boxed{\dfrac{29}{12}}.\]