Find six rational numbers between 3 and 4.

The numbers 3 and 4 can be written as $\dfrac{3}{1}$ and $\dfrac{4}{1}$.

Since we want to find six rational numbers between the given numbers, multiplying the numerator and denominator of the above numbers by 6 + 1 i.e. by 7, we get $\dfrac{21}{7}$ and $\dfrac{28}{7}$, which are equivalent to the given numbers.

$\text{As } 21 \lt 22 \lt 23 \lt 24 \lt 25 \lt 26 \lt 27 \lt 28, \\[0.7em] \dfrac{21}{7} \lt \dfrac{22}{7} \lt \dfrac{23}{7} \lt \dfrac{24}{7} \lt \dfrac{25}{7} \lt \dfrac{26}{7} \lt \dfrac{27}{7} \lt \dfrac{28}{7}$

Therefore, six rational numbers between 3 and 4 are:

$\bold{\dfrac{22}{7}}, \bold{\dfrac{23}{7}}, \bold{\dfrac{24}{7}}, \bold{\dfrac{25}{7}}, \bold{\dfrac{26}{7}}, \bold{\dfrac{27}{7}}$