Determine the value of $\left(\log _{2} 4\right)\left(\log _{4} 6\right)\left(\log _{6} 8\right)$.
Using the change of base formulas for logarithms,

$$
\left(\log _{2} 4\right)\left(\log _{4} 6\right)\left(\log _{6} 8\right)=\frac{\log 4}{\log 2} \cdot \frac{\log 6}{\log 4} \cdot \frac{\log 8}{\log 6}=\frac{\log 8}{\log 2}=\log _{2} 8=3
$$

ANSWER: 3