Answer
$0.$
Work Step by Step
Since we have $$\left[\begin{array}{rrr} {2} & {-4}&{6} \\ {-4} & {6}&{-8}\\{6}&{-8}&{10}\end{array}\right]=2\left[\begin{array}{rrr} {1} & {-2}&{3} \\ {-2} & {3}&{-4}\\{3}&{-4}&{5}\end{array}\right]=2\left[\begin{array}{rrr} {1} & {-2}&{3} \\ {0} & {-1}&{2}\\{0}&{2}&{-4}\end{array}\right]$$
then, we get
$$\left|\begin{array}{rrr} {2} & {-4}&{6} \\ {-4} & {6}&{-8}\\{6}&{-8}&{10}\end{array}\right|=2^3\left|\begin{array}{rrr} {1} & {-2}&{3} \\ {0} & {-1}&{2}\\{0}&{2}&{-4}\end{array}\right|=8(1)(4-4)=0.$$
