We find the LCM of the denominators as follows;
The multiples of 15 are;
[tex]15,30,45,60,75\ldots[/tex]The multiples of 6 are;
[tex]6,12,18,24,30,36,42,48\ldots[/tex]Thus, the lowest common multiple of 15 and 6 is;
[tex]30[/tex]Then,
[tex]\begin{gathered} \frac{8}{15}-\frac{1}{6}=\frac{\frac{30}{15}(8)-\frac{30}{6}(1)}{30} \\ \frac{8}{15}-\frac{1}{6}=\frac{2(8)-5(1)}{30} \\ \frac{8}{15}-\frac{1}{6}=\frac{16-5}{30} \\ \frac{8}{15}-\frac{1}{6}=\frac{11}{30} \end{gathered}[/tex]Thus, the difference is;
[tex]\frac{11}{30}[/tex]