#)Giải :
Ta có :
\(mn\left(m^2-n^2\right)=mn\left[\left(m^2-1\right)-\left(n^2-1\right)\right]=n\left\{m\left[m^2-1\right]-m\left[n\left(n^2-1\right)\right]\right\}\)
\(=mn\left(m-1\right)\left(m+1\right)-mn\left(n-1\right)\left(n+1\right)\)
\(m\left(m-1\right)\left(m+1\right)⋮6\left(1\right)\)
\(n\left(n-1\right)\left(n+1\right)⋮6\left(2\right)\)
Từ \(\left(1\right)\) và \(\left(2\right)\Rightarrow mn\left(m-1\right)\left(m+1\right)-mn\left(n-1\right)\left(n+1\right)⋮6\)
\(\Rightarrow mn\left(m^2-n^2\right)⋮6\)
Mà \(4mn\left(m^2-n^2\right)⋮4\)
\(\Rightarrow4mn\left(m^2-n^2\right)⋮24\left(đpcm\right)\)