Least common denominator of the numbers in the list $\frac{2}{3},\frac{5}{6},\frac{4}{21}$ is $42$. Convert numbers in the list to fractions with denominator $42$.
$$\frac{28}{42},\frac{35}{42},\frac{8}{42}$$
To sort the list, start from a single element $\frac{28}{42}$.
$$\frac{28}{42}$$
Insert $\frac{35}{42}$ to the appropriate location in the new list.
$$\frac{28}{42},\frac{35}{42}$$
Insert $\frac{8}{42}$ to the appropriate location in the new list.
$$\frac{8}{42},\frac{28}{42},\frac{35}{42}$$
Replace the obtained fractions with the initial values.