$[1-(\frac{1}{6})^2]×[1-(\frac{1}{7})^2]×[1-(\frac{1}{8})^2]$
$=(1-\frac{1}{6})×(1+\frac{1}{6})×(1-\frac{1}{7})×(1+\frac{1}{7})×(1-\frac{1}{8})×(1+\frac{1}{8})$
$=\frac{5}{6}×\frac{7}{6}×\frac{6}{7}×\frac{8}{7}×\frac{7}{8}×\frac{9}{8}$
$=\frac{15}{16}$